{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
    "\n",
    "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.12-Gaussian-Mixtures.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In Depth: Gaussian Mixture Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *k*-means clustering model explored in the previous section is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application.\n",
    "In particular, the non-probabilistic nature of *k*-means and its use of simple distance-from-cluster-center to assign cluster membership leads to poor performance for many real-world situations.\n",
    "In this section we will take a look at Gaussian mixture models (GMMs), which can be viewed as an extension of the ideas behind *k*-means, but can also be a powerful tool for estimation beyond simple clustering.\n",
    "\n",
    "We begin with the standard imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating GMM: Weaknesses of k-Means\n",
    "\n",
    "Let's take a look at some of the weaknesses of *k*-means and think about how we might improve the cluster model.\n",
    "As we saw in the previous section, given simple, well-separated data, *k*-means finds suitable clustering results.\n",
    "\n",
    "For example, if we have simple blobs of data, the *k*-means algorithm can quickly label those clusters in a way that closely matches what we might do by eye:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate some data\n",
    "from sklearn.datasets import make_blobs\n",
    "X, y_true = make_blobs(n_samples=400, centers=4,\n",
    "                       cluster_std=0.60, random_state=0)\n",
    "X = X[:, ::-1] # flip axes for better plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the data with K Means Labels\n",
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(4, random_state=0)\n",
    "labels = kmeans.fit(X).predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From an intuitive standpoint, we might expect that the clustering assignment for some points is more certain than others: for example, there appears to be a very slight overlap between the two middle clusters, such that we might not have complete confidence in the cluster assigment of points between them.\n",
    "Unfortunately, the *k*-means model has no intrinsic measure of probability or uncertainty of cluster assignments (although it may be possible to use a bootstrap approach to estimate this uncertainty).\n",
    "For this, we must think about generalizing the model.\n",
    "\n",
    "One way to think about the *k*-means model is that it places a circle (or, in higher dimensions, a hyper-sphere) at the center of each cluster, with a radius defined by the most distant point in the cluster.\n",
    "This radius acts as a hard cutoff for cluster assignment within the training set: any point outside this circle is not considered a member of the cluster.\n",
    "We can visualize this cluster model with the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "\n",
    "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n",
    "    labels = kmeans.fit_predict(X)\n",
    "\n",
    "    # plot the input data\n",
    "    ax = ax or plt.gca()\n",
    "    ax.axis('equal')\n",
    "    ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "\n",
    "    # plot the representation of the KMeans model\n",
    "    centers = kmeans.cluster_centers_\n",
    "    radii = [cdist(X[labels == i], [center]).max()\n",
    "             for i, center in enumerate(centers)]\n",
    "    for c, r in zip(centers, radii):\n",
    "        ax.add_patch(plt.Circle(c, r, fc='#CCCCCC', lw=3, alpha=0.5, zorder=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An important observation for *k*-means is that these cluster models *must be circular*: *k*-means has no built-in way of accounting for oblong or elliptical clusters.\n",
    "So, for example, if we take the same data and transform it, the cluster assignments end up becoming muddled:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(13)\n",
    "X_stretched = np.dot(X, rng.randn(2, 2))\n",
    "\n",
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By eye, we recognize that these transformed clusters are non-circular, and thus circular clusters would be a poor fit.\n",
    "Nevertheless, *k*-means is not flexible enough to account for this, and tries to force-fit the data into four circular clusters.\n",
    "This results in a mixing of cluster assignments where the resulting circles overlap: see especially the bottom-right of this plot.\n",
    "One might imagine addressing this particular situation by preprocessing the data with PCA (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), but in practice there is no guarantee that such a global operation will circularize the individual data.\n",
    "\n",
    "These two disadvantages of *k*-means—its lack of flexibility in cluster shape and lack of probabilistic cluster assignment—mean that for many datasets (especially low-dimensional datasets) it may not perform as well as you might hope.\n",
    "\n",
    "You might imagine addressing these weaknesses by generalizing the *k*-means model: for example, you could measure uncertainty in cluster assignment by comparing the distances of each point to *all* cluster centers, rather than focusing on just the closest.\n",
    "You might also imagine allowing the cluster boundaries to be ellipses rather than circles, so as to account for non-circular clusters.\n",
    "It turns out these are two essential components of a different type of clustering model, Gaussian mixture models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generalizing E–M: Gaussian Mixture Models\n",
    "\n",
    "A Gaussian mixture model (GMM) attempts to find a mixture of multi-dimensional Gaussian probability distributions that best model any input dataset.\n",
    "In the simplest case, GMMs can be used for finding clusters in the same manner as *k*-means:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.mixture import GaussianMixture\n",
    "gmm = GaussianMixture(n_components=4).fit(X)\n",
    "labels = gmm.predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But because GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments—in Scikit-Learn this is done using the ``predict_proba`` method.\n",
    "This returns a matrix of size ``[n_samples, n_clusters]`` which measures the probability that any point belongs to the given cluster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.469 0.    0.531 0.   ]\n",
      " [0.    0.    0.    1.   ]\n",
      " [0.    0.    0.    1.   ]\n",
      " [0.    0.    1.    0.   ]\n",
      " [0.    0.    0.    1.   ]]\n"
     ]
    }
   ],
   "source": [
    "probs = gmm.predict_proba(X)\n",
    "print(probs[:5].round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize this uncertainty by, for example, making the size of each point proportional to the certainty of its prediction; looking at the following figure, we can see that it is precisely the points at the boundaries between clusters that reflect this uncertainty of cluster assignment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 50 * probs.max(1) ** 2  # square emphasizes differences\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', s=size);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the points in the middle area between yellow and purple cluster is smaller than others.\n",
    "\n",
    "Under the hood, a Gaussian mixture model is very similar to *k*-means: it uses an expectation–maximization approach which qualitatively does the following:\n",
    "\n",
    "1. Choose starting guesses for the location and shape\n",
    "\n",
    "2. Repeat until converged:\n",
    "\n",
    "   1. *E-step*: for each point, find weights encoding the probability of membership in each cluster\n",
    "   2. *M-step*: for each cluster, update its location, normalization, and shape based on *all* data points, making use of the weights\n",
    "\n",
    "The result of this is that each cluster is associated not with a hard-edged sphere, but with a smooth Gaussian model.\n",
    "Just as in the *k*-means expectation–maximization approach, this algorithm can sometimes miss the globally optimal solution, and thus in practice multiple random initializations are used.\n",
    "\n",
    "Let's create a function that will help us visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "def draw_ellipse(position, covariance, ax=None, **kwargs):\n",
    "    \"\"\"Draw an ellipse with a given position and covariance\"\"\"\n",
    "    ax = ax or plt.gca()\n",
    "    \n",
    "    # Convert covariance to principal axes\n",
    "    if covariance.shape == (2, 2):\n",
    "        U, s, Vt = np.linalg.svd(covariance)\n",
    "        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n",
    "        width, height = 2 * np.sqrt(s)\n",
    "    else:\n",
    "        angle = 0\n",
    "        width, height = 2 * np.sqrt(covariance)\n",
    "    \n",
    "    # Draw the Ellipse\n",
    "    for nsig in range(1, 4):\n",
    "        ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n",
    "                             angle, **kwargs))\n",
    "        \n",
    "def plot_gmm(gmm, X, label=True, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    labels = gmm.fit(X).predict(X)\n",
    "    if label:\n",
    "        ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "    else:\n",
    "        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n",
    "    ax.axis('equal')\n",
    "    \n",
    "    w_factor = 0.2 / gmm.weights_.max()\n",
    "    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n",
    "        draw_ellipse(pos, covar, alpha=w * w_factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this in place, we can take a look at what the four-component GMM gives us for our initial data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, random_state=42)\n",
    "plot_gmm(gmm, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can use the GMM approach to fit our stretched dataset; allowing for a full covariance the model will fit even very oblong, stretched-out clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n",
    "plot_gmm(gmm, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This makes clear that GMM addresses the two main practical issues with *k*-means encountered before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing the covariance type\n",
    "\n",
    "If you look at the details of the preceding fits, you will see that the ``covariance_type`` option was set differently within each.\n",
    "This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem.\n",
    "The default is ``covariance_type=\"diag\"``, which means that the size of the cluster along each dimension can be set independently, with the resulting ellipse constrained to align with the axes.\n",
    "A slightly simpler and faster model is ``covariance_type=\"spherical\"``, which constrains the shape of the cluster such that all dimensions are equal. The resulting clustering will have similar characteristics to that of *k*-means, though it is not entirely equivalent.\n",
    "A more complicated and computationally expensive model (especially as the number of dimensions grows) is to use ``covariance_type=\"full\"``, which allows each cluster to be modeled as an ellipse with arbitrary orientation.\n",
    "\n",
    "We can see a visual representation of these three choices for a single cluster within the following figure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![(Covariance Type)](figures/05.12-covariance-type.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Covariance-Type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GMM as *Density Estimation*\n",
    "\n",
    "Though GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for *density estimation*.\n",
    "That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.\n",
    "\n",
    "As an example, consider some data generated from Scikit-Learn's ``make_moons`` function, which we saw in [In Depth: K-Means Clustering](05.11-K-Means.ipynb):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "Xmoon, ymoon = make_moons(200, noise=.05, random_state=0)\n",
    "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we try to fit this with a two-component GMM viewed as a clustering model, the results are not particularly useful:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm2 = GaussianMixture(n_components=2, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm2, Xmoon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But if we instead use many more components and ignore the cluster labels, we find a fit that is much closer to the input data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm16 = GaussianMixture(n_components=16, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm16, Xmoon, label=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "comment by Leo: the labeled output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dsR3GYx4DGEy7KGV4va2TgXS2ZJBzfcV9L60tCIjeZJo/PLdyj8fd2d3HYCZDdSJeKK8BgRP23CULeXDl+rImojxp12NafRURx0JKiW1BxLHIZAMH9FEzWog69qgO6ZFIIahOxKiMRzAGTm6eyaK6Rl7a3UpG+SyqmcLcqnqEELxrztFs6e8ho308rbBEEKJaHYny89dfLISmPrVrK58++jQSdoSmWBVbB3pLBJYjJU3x4herNdnHzza8QFp5BU1lfV8nJ0+ZybvnL6HTHeSmVx4jm/t+0srnzzs3s22wly8sPQNjoLYygkobMkIRi1lEndHNZiEhB5pxExDf+MY3eOCBB9i9ezfXXHMNtbW13HPPPVx77bV89rOfZcmSJSxfvpwVK1Zw4YUXAvDpT3+amTODAWqsdZMHs9/CYSRdA6l8iboShjubV27duVcagGVJhDBUxSNBUtywXS4+YTG1lXHufuFVBtKl/oI8EccKwjwNKAXxSJDhnMkGmsTFxx3NXS+sLGsOGomUguPnzSryp9REYpwzbX7xeUtBtR3nuqVv5ZXunWxOBtrCxr4uNg10F33WjmQfv3rtJT5+1Kksqm3kuc7tJZ9rDCytbgk+V8Btm1fwSlcbesR37WrFs53bOKVxJve1rscdITx9o9k60MvmgR7miXoMUFcZQRtIpX0ymUBQxBy7bAn0kJADybgJiK985St85StfKVn+k5/8pPC7ZVl87WtfK7v/WOsmC74yuN7+CwcBVFdESGcUMxpqRt2uuXbIdqm0LmRB74nmuiqkpFB+Ir+bwXDKwtmctGAW1//PvSURR0IIjpjWiDbg+TpXygKMksQcC9sWKGU485i5rN6xk62d3YXS3pFcgl17dx8QlM8wxvD2E46msbpyxOcEmoVtgW1ZQeKaFJiYTSRj8Zb4PN7CPAa9LA/ueL1EECljWNvbScp3eXDHhrLfgRQCDCQzHs93bWdVd3uJcBg6nubFXTvZUkYTgcBMtnmgh3nV9aTSLsYY6qtiiNy6VNon6yoqYjaObZU5QkjIgeGwclIf6lhSIIXYq5kzDGuDqTSuqwuagiMlEUdSEbdZMmcqM6fUsrWzpyh01LEsLjvp6Jz5wrBkVgt3P//qmJ/nWBYXHnskrmdwXb9Q8XTk2QoBV5+1jF888gxaG3ytidgWUdvm3aefULhOCZD/XYJtLDyhSWcVHzr3VNbuaGfFllYcy+LURXM4+ahZbNqxm9Xb2pFScvzcaVTGYoHGJYKyG1IGjuJcNaXiE5OCiphFKqPQBpKeiyUEfpmvWwpBVybNrsxg2e/CYNjtpWiKVPJM17ai3IsydwpjIGE5JFVpNrstJTWRoX4W6YxHt4a6mlghzFApw0DSIxrTJCJ22PI05KAQCogJhBCC6ooIybSH648+4BhjyPqaTNbP5TMUr08TVCetiDlUJWyue9d5/PqxF3li9WYwUJ2IcdWZx7F0zjR8rVEa6qsqOPOo+Ty5dlNh1p6PprGkpK4ywUXHLea4uTMK427eh5ovtGcQhYqqS+e28NXmi3lq/WbWDnZSVRPjvHlHMK26fMRFXibalqQqIUlnJEfPnMbRM6cViuZlXU19ZSXnH7eQeMTGtiX5ohbJjIfnDY302wf6+MOmNWzq66YxXsFl8xazpKEZS1pUJCRZ1yfhOCWZ2XksIZgSjY96Dzyt2ZDspDlaRVp5o24XfD+ChRWNVFoRHtj1Gp4p1hIFcNyUqUXL0q6H6YP66mjBB2GATEbheZrKuBNmY4cccEIBMcGwLUl1ZQTX02S9YDAY7mBOZX0G0y562BiTb3ATzGtzPw30J118o3Gk5BOXnMkVpxxLxvOJRWxe6m3jJxufp9qJ8pbGuTTFKnn3GcdxzKypPLZ6I6msy9I50zlz8VxikX0Lr80zIF3u4DXcuEK7hifWbWdJdTNfWHgG9rDKqoXJcK5PgyUFsRoHrTSu72MIIpxqq6KYnPAKynMIoo7AGEFlzMFzAu1j7e5ObnzxsUIJjd2ZFBtf7ua9C5dy/qwFSARI+PaqJ8qafBwhecfso4g7ERbWTGFtb2niIMAjbZs4fcpcZiVqeW2wfIkSC8EZ9bOpi8SpdWL0qDTPdm1FaNDKIJVhWXclPbuSNE2tLvKlZFyP3f2GhpoY1jBtSClDf9KlKuGEJqeQA0ooICYgAkHUCSJYtAkK7w2kPXqTWdysnxvg8m06QalAC9BaF0pY5wca11M01AQ9m23Lwsbw/159kPbMABntYwnJnW3r+Pi8kzircS5Hz5zKUTOnDlVlJUjuygcsaWNGtbWLnJgKzPOGf177KH1esR9iVX8Hf2hbywfmH4+UoqB9WHKo/8LQIGmhjU3WU2TckSU5IOv62JaTm2ELHMvCSUh+uf7lQi2mPK5W/O+GlZw1fQ5Ry+aRHZvoy6ZLrkUAb5k2j7Na5gJw9fzj+IcX/1T2erUx/HbbSs6begSbN/YUaQYCqI/Eefes46gSgflICMFF047Efrab1zvaIa2Id/q0iz7+59lWrvriJUydVlvkC3Jdn+6+DA3VsaJoJmNgIOVRlRA4YcmOkANE+GRNYPI+hr7BDOmMiyMFkYhEWiI3uIqibUWuh/L2TC+b011BgpcJusDlezH/vnU1rek+MjoII1VG42rFf258jl0DSZIZn1TGI531h/65wQCd8YJaRL5vULl/2gdM8CBJKYKidpbkteRu0qo0VNXVivvbNxCPWERtScSSOJYM+kNTWi5bCkE8YlNTESHqWMWRPKL0Ac74iu0DfWW/T4lgS38PAC/sasUtY14ygIciEbOI2IKGeBxbjP6arOvtpKkywYfnncSCygai0qLGifG2GYv42yVnM6OqtsgT0r97gPaXtpPYmiWxy0eYoAe3m3F54s6X8MvkvWRdn+7+bEn+RiAk3CLfUkjIeBJqEBMMY8yQ1pBy6Rtw8ZQqWxZDCrBsAQT9DTYlu/n3jU+SUh4S0MDV04/lorojgECI/LlzS1mHqhSCtZkO3tI4t7Bt3nCVRyBAmJK4/HLnllLeqGGZSd9FG12UvbwnpBBUJSJkKiJk/aBAYdSxGPkhtpRIRFktRwMxO3jkK+xI+c9BUOlEAm3ECgTSSc3Tebq9NNQVgizsQVyOqG9gfl1d4XSMgQEvy5/bNrG6dxcxaXNi7UwqN6fLhxMbaH2tjZ6BQFsYuUXG9ejpg/qa4nXGQDLjU1PhUOKUDwnZT0IB8aZi8FWuz7MOqrMaE8zQ+1JZMtnRQ16L23fCoJfhn9c/WtAM8vx6xyvMrKjhnCnzsYUsWZ/H1UHl1Xw3tdEpX8XUGMPGwW7aMgNMj1ezsGrKqA7g+ZX1KA3yDZjPpRAkIha1lREsIci4Cs8fqmRrS8kp02bwzM4dqBGCsCYaZcnUJrQxXDhnPmt7dhWS1vLYUnLWtDnDrgvef+TxowoIDbRUVlLtROgbGOqT0edm+M6aJ8kMS5rb1bGWedGqUcuJ2I6NVoaegQwxS2I8n3hlDJlzRqddj+7+wHE9XMj4uWq8oT8iZLwJBcRBxaB0kHPgK4PvF2sGQkDK1fQPZorrE+Wc0IH9PzBJ+FrnCu4F/oYneraWLwlhFHe1reOcI4LEsdGGfwPEpEM25wR2tY8ykLCdwudbcqROETDgZfn66kfYke5D5pr2zK6o5azGOTy5eyvZYf6AiLT46IJlONYbm+06Od9MPsLKsa0g1NdXZF2FUoZPHX8yW/p66c6kyPg+UcvGlpJ/OP2tWFJiAWfNms2ank4e2BzkQeTH7KuOWML0yuqiz6yORLlo1hE8tH1jUV0mSwhmV9fSnKgEARnHIeMFEU1/2vk6ad8r0mQ8o9loDTCzQmCNiHaVtmTBsrmseGg1qx5djc73nXAsTr/0OE664BiEEKSzHj0DUF8VZbjG4GvDGwslCAkZnVBAHGCU1kHP51zfhf5shofbNrEzNcDCmgbOappNxApuQ3/SYzCdGzlydR8CJ7RBKZVLZiv/ObvdJK4pr3Hsyg4ymPJIZvwS520eC8FA1qV9MMnPt73A6oEODDA9Vs2HZp3IgooGhIR41MIaYRr699eeZEuqpyh/Y9NgD7V2jL+cfTx37lzLgJ9lfmUD1yw4kaUNjeyrOURKSTxm42dLH1lLBn6KeMTCU4Z4zOJHF1/G8ztb2djbQ1OigtOnzyqYlyBwGH/iuJO4ZN5CnmvbgWNZnNIyg4ZYHF8HzZeUGnL4v2fhUvrcDC/uas0VPDTMqKzhr489PTiggeoKB7fPRxvD2r5dozrzp1w0n/7fbgjMib7GjlhMmTmFzGCG157bWJRY4nuKJ+58GSEEJ10QFFdMZTwQgvphLUz3NskxJGRfCAXEuGNQKiiPHZg+hgb1dX27+dIL96OMJqsVccvmp6+9xPdOfjuWskhnAo0i6B09pB2MRS6hl1nxWqLCIlsmxn5OvA5tNFobmqOV7Mj0lxzHlpLGSAVff+0h+rx0wSG6PdPHTa//ma8tuoAZiWpGDuy9bobVfbtKkvt8o3mpt43PLDyNS6YvxLatoCXnPhSgEyIo7RFxLBxLEIvYjF2WTOBYAseSJKI251fM4y1Kk3VLe1/kmVldw8zq4mxz24JgOm7QJtcAyBi+sOx0diWTbOvvoyGWKGga+eNaUlKVcOhLujij+FekEDS11PPWL1xC69odeGmPqfMaqZpSxf/9y51lS9ZqpXnmvpWceN5RyJwJMJV2g9DfikBIOFZoXgoZf0IBMS4M9X92fV22eYwxhq+98jCpYUlVaeXjKsWNK5/gUzNPQ2lNWvmsGNjJoO8yL1HPnFhdSdasyIWCtmcGeaxnE11uijnROuLSwVO6aObqCIu3NS8q/H1FyzH8cMuzRdqGLSQt0Sq63CQp5ZVEy3hacd/u9Xxm4aklJqZBP4slZFnHtyUEWaFoijn7LBgijoVjW/tR+lpgWwI7Jyx8FZj18t3zjB6tQlXxMaQIOsJBUO5jTrSWuQ21gbkvX2Ik13jaAIm4hbQkZ7XM4d7t6/FG+GEMhmMbWojbDlWnHlE4h47NnQhLBsWpyuBlfdyUS6xyKON6MBVom1MbEmGoa8gBIRQQ+0EgFNSoQmE4rw90M+iXlllQGFb2tZOe6rE108sPtj8NxuAbjSUk8+L1fHLmqUQsi14vw6r+9sDUpA2/716NyuUlrEt3EhEWR8Qa2JDpwmCYHqnhisYlTIsN2dRPqJ3OX848nttaV+KawDG9pHoqH511Ene1ryVbxomtgU3J7rL+h+ZY5ajRSo60mFlZtVeDvBBg2xaOJbFtUT7S5w1iTDC7tyREHQuDCcx2WuN5Gs/PaWv7cDyBoOBGGfEFNFRLLpi9gLW9nWwd6CGrFbaQCAHvnX88UWmXlKVP1MQxY4SrSkviS6tQcTb/scYYfE9DdNRdQ0LeMKGA2GcMXq6onj9GOYyRuNofc9Bztc8Ptz9dNEAro9iY7uL+rteIS4c7OtcgERhMyYzdMwrfKBxp8c05F6ONwZEWli2xRgxgZzfM5cz6OXS5KRKWQ4UdQQhoSVQSlVaRUxkCo1JLrHyJDEdavHf2Un69ZUXRflFp8ZEjTsQaIyqqSChYokRTOlCIYdpF1GGYwDAFTUMpXbbO1N4QtSX1FXE+v/R01vfuZn3vbioch5MbZ1ARTbC7J1myT1V9JVNmTmHXltKsbSEFC06aRzLjYduyULQvGglKgfcms0gZlGkJXREh40koIPYSbYKZZtZTe9QWRuIrzXSndtSy29Oj1WxMd5dd6xnNo92bcgJgbIFkgLWpXUhEYWCOlAl9FCIo6DetqqpQOM8ScO7Uedy2YxVQLCAi0uLyGUcV7W9JiWVLbCG4esESmhMV/HLTK+xKJ2mOV3LNghN4y9Q5pZ8tJY4d+Aksa3w1hTfKkMAINAwItASldS4nJRAaWpvCzH+sgdgYqExESGd9jqxr5Mi6xsK6eIVDd58o29jqtHeexJ3f+WPJ82W0Yf3Tr9G6tpW3vOsUjjttPgnHCrTH3In0DGSRlqQiGr7SIeNH+DTtAWMCoZB1/X2enRkMGVfjeQqJ4Np5y/jPjc8XIokkAkdI3ttyHB3uwKiRKCnt7fUwqjD8164XmRat4fSa2dRHE0QikohtEY9ZhXIW5QbmCjvC1445j5vWPc6Aly0ky318/kkc09AcCBOCgXSks/q8afM5b0QPBghmv3ZOQwjMPG++QNgbRK46LAwJWSHyDushx7U2Q9qHMYYged1gEdSO6upL5ZYFRCyLipjDQMot/gYFrH1yfa7cYRkfloaB7iT3/fzPODGHo46bScwZEv7aGLr70lh1iaLlISH7QyggxsBXmr5Bt9DtbF8wxpDxAuGQZ1nVTP56VoQHujbQ6SaZE6vjwilH0BSppMqOosYwaOytbBLAq6kO1qU7eaxvE9dXncORdiOxqE06uWdH5oKqen52yl+wLdOHp30W1TQUwnD36vNFrgdDTiCUEyaHKsYE4bGWoKygy/sE8jWyaoCILRlMe4X7V1URQesEEccqKpEhMGxdtR09SnJhHt9TPHfvK0yb30RdVYyoM3RPlTbs7k3TXJ/ACSu9howD4yYgNm/ezHXXXUdvby+1tbXceOONzJkzp2ibL33pS6xfv77w9/r16/nBD37Aeeedx/e//31uvfVWmpqaADjhhBO44YYbxuv09pmMGzRpiSXemPfPECTC5f8azPgMpj3mxuv5+IxTSrZvcBKcXjubp3u2UhpHtC+fG+AbjW80/7HhGb5/wqUl2wUltHNmHhEkwcncTxAcGWvY42cJQa5taCAMpBzafzISKIBBAcK8A7u+KkbW03i5Z8G2gl4VlXGb7v4Mfs5kaUfsvTZddrX1orWhdyBDXXWMyLAIJl9pOnsCIXGoaGshE5dxExA33HADV199NcuXL+eOO+7g+uuv55e//GXRNjfddFPh93Xr1vHBD36Qs846q7Ds8ssv58tf/vJ4ndIbJjAp7V9nNykksahNxlUMpnyS6bF7BmgDl9UsJqoc/tT/2h6PbyGotmMsrmik002yMd1dNjFrt5uiR2VotmuIRm2sXG8FOUpW9GgMFyi2JbCERFr7dozJiJSC+uoYnT2pokz37ECGP/7kEbau3YkBpkyvp2V+E9vW7tyjoKisqwACjaGnP0NddZyIPXQfXF/R2ZumqS5BKCNC9odx0UO7urpYs2YNl14azFQvvfRS1qxZQ3d396j7/N///R+XXXYZkUj5omlvFgZD1t13k1I5IrZEiKA1Zixi4zgy1/VMFNptAmSVpi+ZJeNpjk1Mwx7jtlTKCFUyylsb5nPDwvP4yJyT+ficU0oilfIICLrLxWyidvD5lhzbOZyvDOs4FrGoTUXcoTLhUJVwSERtIrY1YRzMhwKJqEVVxdBz7rk+P/rq79mydmeQwKcNndu72PFaWyERbjTsiMWJuYxqyAmJgQzuiLZ4Gddnd1961MCIkJC9YVw0iLa2Npqbm7Fy2ZyWZdHU1ERbWxv19fUl27uuy1133cUvfvGLouX33HMPTzzxBI2NjXzmM5/h+OOP36fzaGio3PNGe8AYQyTmFjmM3+hx+wazWL6hti4BDBledC5+0vcNg+kstmeoSEQBQzOVTOurZnu6uH+xAOYmGvj7heciJDTUxLGkCGafJkHjlkp2pkszpBvjFRwzY+qo1xFoEwIr/8/KRTVNUBt2Y2P5cNuJTk1tBTt3D+J5mk2rdpBJuyWagvJ02VBfaeUKJBpDy/xmFh47i0Rlcbc7H6hJRIlFil9pJSya6xPIcVYlDtX7MJLD4ToO5DW8KU7qBx98kGnTprF48eLCsve85z184hOfwHEcnnzyST71qU9x7733UldXt9fH7eoaLBs+uK8obUi7PsrXNDRU0tVVvi/xaAgByYyibzAzauSTNtCfyuJ5pf6G9005nu+3PolnFFmjiAqLiLR5T8Ox9PWnkZbAptjSf+2sZfzLhsdQOd+DLSS2lHzp6DPp6U0xpaGSvr5Urv/zUB/oQ0kLaGysorNz7GIbExkbgy/gtVXbcTPlTY7lItn0sMKNrRva+clX/o93/c3bqapNFG03OJiloSqKNawQYk8vDA6mCyU5xoND/T7kORyuY3+vQUox5gR4XKaJLS0tdHR0oHJlApRS7Nq1i5aWlrLb//a3v+WKK64oWtbY2IjjBPUozzjjDFpaWtiwYcN4nN4+Y0lBRdQmEXOCvsf7OPtKZscWDr7W9CQzZYUDwBSngq/MOo+3paZz4h8HWfaHPj7UOZt6KyizUBjcBYUBf1FNI98+9u1c0rKI4+paePe8Y/jf897NqTNmUJ2IUFMZJR6xiTpBYtqezEwh40/UltRWRalvrsF+g6Go2tdkkhke//0LJdV7fV/RPZBFjZgk9Q1mSWZG788REjIa46JBNDQ0sHjxYu6++26WL1/O3XffzeLFi8ual9rb23nxxRf59re/XbS8o6OD5uZmANauXUtraytz584dj9N7QwghcOxck5qEUyjTXRQHnwtJHP6epj1N/0C2RDikepM88fMHWfPwKoQlOfLiEzj2itOxc/2eg2Y8gVYghWDF7Y+z/lePoDyffm146M8bmL50Du/85odIVDhUxCMIY8hHzQAkolV8qOIEEgmHhqpomFU7wTAG6qpinHbuUTz8uxfAe4OBEAZa1+2kP+lRXeEUNXDyfEXPQJb66ljBQW0MdPVnsCwZ5kiE7BPjZmL66le/ynXXXcfNN99MdXU1N954IwDXXnstn/3sZ1myZAkAv//97znnnHOoqSmuoPntb3+b1atXI6XEcRxuuukmGhsbSz7nzSEI37TKdLjJd4AzRuApxWDaJx7Pfa25ATrVn+KnH/h3BrsGULlwx5dufZQdz73Ge3/wCaQlMYX5vKFn226e/9XD+MPyL7y0y44Vm3n1vhc546ozEbmQyuAchp2pgMqYHQqHCYolBbNm1vLh6y7l19+5n2xuZm9yiXf+3kbPiUBj6E9CTUWkMEnYuraVVx9fTzblctSJszn1gmNIVMbQ2tDVm6G5Pl5IAAwJ2RPCHEaF5MfLBzGcvbXx+bkkpXL1mR768f089KP78UdERznxCJdc/17mnx74YvJVQZ/970d4+hcPocsUb5t65Aw+879/O2oiVDRi0VgbL1ke2lsnBvlrSGZ9dnUn2bl5N76vmD63kbZt3fzyX+/BzbiF51hQWtZDSMGcY2ez7B0nAkE9q5qKCM/c/RKrHl+HypkuLcciURHlU9+4gsqawF8RjVg011XsV/jr4XAf4PC4jgPtgwgzqccBY4J49PLF+wyrHl5ZIhwg0Aq2PLuelsUzefh7d7LhsVcxylDRWD1qRq3yFfYo3diEoCicMmTiUhG1qa6IIuYNacnRmI1WKjdRCJYJSxYkhNEGy7GIVkRZcv5QqKvvK9av2MYrD68p+gzlKZIDGR79w0tc+sEzAci6iq7+NI01pZOIkJCRhAJiHOgezJZNrBvs6ufBWx5i18b2svtJSxKpjHHrJ29mYFdvQWMY3NVXdnsrYrPkouODUMgyipLjWKGN+RCiriqG6ymyOV/Evb96EjdTPJHQSmPZkiNPXcBAb5qmuY3MXDIT2xl6dX3P57Fbnyz7GVppXn1+U0FAACTTHo4lqa0Ma4SHjE0oIPaTvqRLOl2qHQx09fPtK24k3ZdC++XtytKSJGorSfUOlpqTcmUs8svtqENVcy1nvPesUQszTWztweB6QXVUK1/ee5JHUUkBU2rjtHclUdqwae3O8tvZFrOPnEbjgqmkymTkt65pHTP7WkiBr0yR5tmXzOLYkopY2Mn6UEcIyHqajOtjSUkiZo3buxUKiDeIEDCQ8gpdvYpXwgP/eT/pviS6jNnJyiUznfvX72D35g68dJljGKhsrKZ2+hS8tMuic5dy/PJTqKqtKCsgIhGLeMR6Yw0MDgIZV5EaNju2LEll3B6zX8RkwLEk9dUxdvelsSyJX65nuMn5E6J2rsFR8TbJ3lRZf1WeI0+eT89AlobqGPmv2xjo7s9g2xbRsBvdIYvWhv6kR8bLV5tW+EpTU+EwHjXRQgHxBkllFX2DpeGsAGlXsfaRVWWFg5CCuacu4q1/vZxoTSX9tz+GFbVRIyvGCmicP43L//kDhUXVldHRtYdEZMIKB2OCsufDUUrTn3RJRB2ikcltFquIOWQ9xTGnzGfl06+XDPZSClrmByHglQmHvkFdFIxR01SNHbHL+rkicYfjzj0az1f0Dmapq44Who189depYWG/Q5b+ZJb0iPue9RQZ1yI2Du9VOHV4A3hK09tfPhHO9RUDSRc7Vt7cYzk2U5fOw49GSaZcWo6bX1aQ2FGHZe85u/C3lIKIU/52ORGLeHTiDrKe0mWd7sZAMuORfgPl1A836qqiXP6hs6hrrCISDcw+tmPhRGwuuubsQukTSwoSI8xCLYtaiCaiJQmd0pJc9onzcXIaa8b1GUgVm6g8X7G7LxPWbDoEyXiKzChh0RnXH5fEyFCD2EeMMWWzVSHIkO5LBjV2jl1+Co//6D78rFey//STF4E2dL62gwf+4ZdBQb9h21gRm7d+6hJmLJ1TWBaP2qMW5KuewNoDjN19DSCd9ZECopHJ+zgKBLNn1PK5m67i1ec2sW1DOzUNlSw9bSFpxLDS8RCLWHjKJpsTrFJKzv3IW3nhzhdp39gBQEVdBSdddgL104uTVZNpF8cSxId1nktnPXoGBPVVsYNwpSHjgVKawZRHXbS8D8nPNbGS+yklJu8b+QbpTbp4ZaS2xtA36Bbq5hy7/FS2PPcaO17ZjJd1sWwLhOD0v3oH8dpKjDE8euPtpf4HIWhZPJNjl586tEgKYrHytyoWzWkPE1hA7E1uSjLjI4QgMomjsGxL0tRQwZJT53PMKUPd+aK+prs/U/Q9VsadYBDICY5YZYwzrz4D3/PRviYSDzTYgbRHbWWkYFYyBvqTLpZlFZUIH0i5RB0rdFofEhgGM15JqZXhaGPwfEPUGV1AmFwlhrEIBcQ+MJj2SKZKo0gMhr7BbFEehGVb/MW/fIidq7fy+tPrEVGHuWceQ6KhGoDerbvIDqRKP8QYdqzYzL3/dBtv/fSlJGoriEdtbFka2ioEVFdMbO0BGPNBHk5QL0jgTGKnaUXUxq2I0juYLSyL2pLqRIS+5JDPSwBVcYe+pC6KYLIdG4aN8cpXDORKchSW6eB5bagpLsfR3Z8hkqvVFTJxcf0gInBPeEoXdRyEoY6HhuCnlGO/m6GA2EtcX9GfLBNtRBDN5LrlHdL1C2dyzKypJYO48hVjGQnXPfgKrSu3cM2vvkC8Nl5WCFTEHaKONeHLapQrYV2OwCfhl9QXmkwYAzWVEVxPk8qZJw2QiNn4SjM4LMzVsQQVMYfBtDvmJMH1fJIZEZRgyS3zfEXvQBmndV96vzOtQw4chsBMuDevfFA8NRjih0oCDa2XQuzx3QynCnuBNoae/mxZU0kq65POlHGyCsi4mlTGK/vy1s9tRlqjm1OMNqR6k7z+yMqymdOWFRQSnOjCAdinwUZrTTLtTWqnqUDQUBPDGfF8VFVEivo9GAJ/xHB/wmiksx7uiGCIvNN6+O3JuoqegUxY+XWCknUVntq7dyMYrwxKa5QuFQ570yMkFBB7QGtD76CLVybSyPVV0YyugICMp0mOMbOTlsUZn30H1ihOJgA/47LtxdfLHqO6InrIhCburQaRx/M1mez+tXw91LGkoKE2VvQSC6C2MoptFwuOiphDxBldSAx2D9K6ppXtmzoL5r6BniR//s2z/Ojvf8MP/uG3rHhqQ6EXxWDapT/lhkJigpGP+tvbjT2l8ZUpmUTurXCA0MS0R/qT2bLZqxpDZ+cAm55ZDwZmLzuCaGUQBZLxNIPJLIPtPVgRh0R9+Y5Ps09dzGXf+iiP/PNt9O0sbc8qLUnd1NKGSU7EIhE7dJy5wx9FrQ0du/uRlqCpvmpU4ZHJ+ti2nNT28HjEoq4qSvewkGopAyHR3Z8u0mirEg59SVMU7aR8xTP/9yztGzuCisHaUD2linPefQp3/+hh3Gyg3fZ3DfK7Hz/K5rU7ufwjb8EY6BnIEnHsMIluAuH6qmz0ZBHDTElSCrTWRW1s883C9pZQQIyB62tS5fwOAp78zVP88cbfIXMDmPYV535uOUe+7UTWP76Gp753B9lkBqM1dbObecvfXkH1tIaiwwx09ND63HqajpjGwK6+kpIclm1x8hWnFX+0gJpE5JAqU5GPz1/9+k5+evuTgdkNQ211gk++52zmTG8o2ccAqZw/4lC61vHEGKiKR/B8XeT/itiCmooIvcMSNYUYEhL5RLsVD6ykfWMH2teFXJuetl7u+s+H8LKlNZ9efHQdxhgu+9BZ2LZFVy6JbrzblYa8EUzuvRlji1zJ+EBAGLQOOldKhpqL7as2HwqIUTAYegezVFSWxoZvWb2DP974u5Ichz/92+947am1bHvuNfSw7MaujW3c++Wf8a6ffg47GoQfbnpsFU9+7w4wBuUprFx4pxOPBHkRWvOur76XprnNRZ8Ri9njkiF5MJFC0L67j+/96lFcb+h72dU1wI0/uZ+vfvYd1NckSrQFpQJT097Y2A9n6qqi+L4pOK0hyIvxlWEgFfRP3/jKVlY/uYFsxqVl0TTmnTiXLS9vLZuEOVI4DOelx9aTHsxy9ecuwvUV3QMZpowSJBFy8HB9g68Mrb193L/2NToGBjlqahPvOmUpA5lM0GLYskZUAhZFXSffCOP25m3evJnrrruO3t5eamtrufHGG5kzZ07RNt///ve59dZbaWpqAuCEE07ghhtuACCdTvN3f/d3rF69Gsuy+PKXv8w555wzXqe3TwgB/UkP11VUjFjnKcXTv3kC5ZW+ZEYbtjyxpmQ5xuBnPTY/sZojzjue7GCaJ793B2qYEMkLiVknzOfYS5dx3DlLiFUUCydLCmoTh14FTkvCA0+uxVelfgVfG5548XXOO20xESfI6RiuMWRcn4gjJ3XNJkHgj/C7NO4wLbMq4aC05q5bHmPTim2FUhu9Hf1sfHHTqCXjx8TAhpXb2d3Wy5SWWgbTHo5jUVtxaAREHK5kXJ+nN2/jPx57Cl8HRS9X7Wzn1hdfCTQDBMfPmMZHTllGZTTIqs9rDPujAY7bW3fDDTdw9dVXc//993P11Vdz/fXXl93u8ssv54477uCOO+4oCAeAn/3sZ1RWVvKnP/2J//zP/+QrX/kKyWRyvE5vn8h6isFkeb9Df8pjYFffmNUzy+FnPPq2dwKw4/nXCqap4ShP0b5uBye9fVmJcICgFpM1Si+IiY2gtaO3bBSY7yvaO/sBcD1FKqOKIpiMIVfkb3KPTpYQNNTGSwITBnf1s2nF1qI6TMpXZAYzRbbnfUFakp1bdhf+7hvMjlrSIeTAo7RhIO1y8xNP4ypVCDTwtcaYYL2vNS/t2Mk//ekRhAgmk5YQyP00z46LgOjq6mLNmjVceumlAFx66aWsWbOG7u5Sx+to/PGPf+Sqq64CYM6cORxzzDE89thj43F6+4TB0DPoFm6Cl/ECm66AVNrH9zSzly3A3seMUzsWoWZm0BxGKz3qbEz7qmx0UixmUzFKNvWhwLwZU8pel2NbTJ9aW/jb8xXpjGK4QPB8TbZMnslkI2pL6mviRU7G11duR5UxIxllsN9gfS5jDDX1Q7qz1oauvgzj3KwxZC/Jeoq17bv26ItTWtM5mGT9rt3B5GAcwtDGRUC0tbXR3NyMlYvbtiyLpqYm2traSra95557uOyyy/jwhz/Myy+/XFi+c+dOpk+fXvi7paWF9vbyjXYOFPkS3p6reO2pdfzrO77Bp4/4JF85+W/5zT/cSm93oNEcdeEJxKsTJcXRRj9wUF9p7plHAzD/1EWYMuWZpSU55tylJcstKairOPRMS8O59JxjSsIzAWxbcvKSuUXLXF+RcTWtHb1871eP8Jlv3MZn//l2fnv/y+PeUvZQozJmU1M1lNxmO9aoJoSq2goSuVajwxFSUNNcM2qVhXhljKkjfF+ur+gdzOzPqYe8IUyh5tbeoLRmW2/vuH36QZ2Svuc97+ETn/gEjuPw5JNP8qlPfYp7772XurrSUM43wli9VfeGZMYj6Rt2v7KF//rrn+JlgsgR3/V5+Z4X6NjcwTU/+wwdqzZzzIXHs33FZna8urWs9UNIgXQs0FA/t4kL/+G91EypwpaSmhm1nPnh83nqvx4ufIYdsYlXx3n3V95FbX2x56O2Kjou3b8aG8uH2x4M6uor+MfPvYPv/tfD7OoawGCYMbWOj73nLUxrri3ZfvvObv7ph/eSzdW5H0xl+Y//fozXtnTydx+/8OBfwDiyv/ehvt7Q0Z0imfY444JjePh3zzPSAGRHbI5/61HMO2YGv77pbjKpbGAWNYZ4dYJ5x86mekoVrz6+lu4dPdiOBQIqaxO8+3Nvw0hJVVUMe1iyngCcnOb8Zj5L48lEv45MxsM1gpOPmIl4eM/bO7bF/GlTaMiNIbWVUWL7EeQxLgKipaWFjo4OlFJYloVSil27dtHS0lK0XWPjUP/dM844g5aWFjZs2MDJJ5/MtGnTaG1tpb4+qD7Z1tbGKaecsk/n0dU1+IZnmNoYOvsyeK7i//7p9sLAnUe5Pm3rdvD9y/+Zwd39eGkXO+rkoo9EEGLmK6QtkZbFeddfTcWUGuyIXai/lEq51FRESA5kWHb1W5lyxDRe/t1TpLoHWXT2Ubz1/W/FRCL0dA/5XuIxG9cWdJZrKrQPTIQG7S1TqvnGX7+D3v4UUkos28bzFT09pb6mX9/xDJmRde5dn/seW8NlZx9N85Tqg3Xa48p43QcLQybtIiIWF77nVO7/n2fQOghxdSI2U+c1Mvf42UhL8r6vLGfz6p1sXrODjS9sIj2Q5pUHVyEtyZRZU1j+t5fg9gwSr4rTOLMeIQTdvUncrBvU+hrGwECGIxdMYaAvvd/X8GYzEd6JsdDGMJjygkg1rfnoqSfxn089W3BSj0QAMdtmQU09Xd1JhADt+WPmEkkpxpxYj4uAaGhoYPHixdx9990sX76cu+++m8WLFxcG+zwdHR00Nweq69q1a2ltbWXu3MC8cPHFF3PbbbexZMkStmzZwqpVq/jWt741Hqe3R4SAwaRXqNK6c3351o/K8+lt7So4qPNhrnYswqK3nUjP5nbq5jSz+NJTqBqZ4CaCjNfhJbvnnLSQOSctJBK1ypqQLCmorYweNlkAjiXxfU1tdWD2SI2hOm/avrvscksKVm9sP2QFxHghEEypidHRrTn1gmM4YulMVjy5gWzaZdZRM6ibWU/ehiSlZPbCqTz8308Uhb0qrdi9dTevv7SZ0952XElJl1TWIxq1Cs+snet419WbJnK4PJQTkHzdJKUNyYyL1hpt4MSZM/j6xTU8sH4Vnv8CUmR5dvs0LGlQWtJUWc0Xzz+/KOJvf1NYxs3E9NWvfpXrrruOm2++merqam688UYArr32Wj772c+yZMkSvv3tb7N69WqklDiOw0033VTQKj7ykY9w3XXXccEFFyCl5Otf/zqVlftnMtpbsl5QWz1PdVMNmYHSGZIZpQaKEIJpx87l5I9cNOpnxKN2UFlxZNq7HdRUKkd11aFTTmNvsEfMZGxL4A4LFjPGkEy7RCM2sahdlDNRQAgq4hO59/bBw5KCxro4u7rTNDTXcO47lxXW5dvh5h+3zat3lPVZKl+x6YVNnHjBEmxraDiQArSGjq40dZVRpARXKCKORTrrk9Wa6jD0ddzROqidpI3B9RWepzHkEt2AuniCr5zzRxrizyCFT9qz2dBVT1XEZWp1LVvSf1F0vH1NjBvJuAmI+fPnc/vtt5cs/8lPflL4PS80ypFIJPje9743Xqez1xiCchrDVbZzP3oBv/36bcW9GoQYo/ONwR8jy9GJSBJRu9RXIaA6HsEucxPjcZuKwyxBzMol7gyVjRi67lfWbucPD77MYCqLABrrq0hnvJL+y5YULJw79SCe9cTGsSRTamPs6kkVlWGoSjgYKPRM9zLeqKHZvuvjepp8io0QoKHQ6a8/7VKXEwZZV+F6mmwmSzRqE5nEpVDGk+Fag875itJZhSEQ1kKKnA8pUxAOAHHHZ+nUXQAokyYituGaWQDjUoHg8BqB3gBpV5UUhjv+kmV0buvk0Z89CARhqYnaCmqnN9C6akvJQK99zdQlc8oe33IElfHyIbEVsVw/5hHHs21J3Tg4pScaUghsSxYKHwoRCIy1G9u49a5ni4TBrq7+QgE6g8GWEmlJPv+h8zAmqHU/mes0DSfqWNTXxOnqTRdNdKoTDhjDYNpj+hFTy85vhIDmec1orfE9zarH1rL6ydfIZjxa5jdxwkVLEU3VZKIW0VwUWtYLhERXX4ap9fFJWwplf1Ba8+zm7axt76Q+keAtR8yhIhrBaFMQ9J6nsAQIKbFtwWDKR8jRJ6LGWFhiYGg8ERNIgzgU0cYwMKwxSx4hBFPmTwPAKI1Rmmwyw0BnH04sgu/6hTBVO+pwzBVnEKsJogayAyle/d1TbHlqNZZjc+w7Tub4y0+DEdU2IxEZCI4ylRbrqqKHbT+EiG0VBIQtBVJI7n10VYmmoHKq9rvffhKZjEtlRZSLzj6abE6rS2d9nITDnjpiTRYqYza6uriwHzBkBmqsYuGyuWx4aTN+ztcmpMCJ2Jx0yXFEIxYP/NefaX2tHd8L1m9dvYOdG9q57DMXBR3oqq3Ct511g3ydvkGXuqpoaGraBwYyWT5729209w+Q9nyitsWPnniOf7z0fI6a2hRocDpIF5VWUEVAa4OnNcZUklWNxO3SFAKBJqsXFC2TYxk+9oJJLSCSab+kjLcxMDiY5ndf+e+iUhh+xmOws5+F5ywhlcyy8+WNCCGYsewIjnzbSQBkB9Pc+bkfke4ZLBTee/InD7DpybVc+e2PInLOI8uWVI+S1xDU/J/4TYDeKI4tC2YmYwKzU0fXaJEkQTXKM5cdARTLUt/XuL4mUia3YjKSL+yntKF3oHjSU10ZwQBvefcpTJ3byMo/ryObyjL9iKnUNdfw4M8eZbA3VSjyN3RQ8F3Fyw++ylvecxrprB+YSsm1tFRBEcHAvxbeh73lh489y46ePrxcKZRsbqz4+r0Pc+s1V+FYFq5S2JYMJopC4GUVxkBD7DEisruoSCOA0lG29X8MYw2NK+NxRyatgFC5QmcFTJC6rrTh1T+vLuv+175i3YMrctsHd2jb02vZ+fJGLv3WtWx+7FUyfcmiqqx+1qN93Q62vvg6c05aiJCC6kRxNFOeWMymqsI5bIUDBH4HKxfNBIHAqK2Ks6u7VEgYY8h6Hq+s3c6MqXXU1VWgtC5EaaSziogtCbWIIWoroyXPtiDoUmcwHHnyfI48Oeh3/dKfXuWFB1YWNIpyGGNo39gBBHlCwwWB52lsW9Ddn2FqQyI0Ne0FxhgeWrepIByGo7RhTfsuTpw9HZXxhkqlGMi4ioS9hYV1N2HJ7IhjCjb2foqezKXUDEvr2F/zEkxiAdGXcgs5E4YgU9QYUMaQHquF44jRW3kK5Wf401f/m3RvskjryOOlXTY/s545Jy+kqiJSdtZb8DscxsIhT9QeEhC2FFx45lH85o8v4HpDA5UgsNPe/fBKhBAorTlu8Szef9nJ1OQq7Cql8XyDY4cDUwED9dVRlC4uD51vNmR0UPjNc31e/NOqgjlpLJxcUyulDMm0T30uglsbg+8ZBIr+pEdtZRjVNBbaBA7ockUrARAUBMfweALXVyhjaKn4A0KU+iAMggpnCz0jrOXSEvt9Pyally/rKdK5l0cbg+uqwheZyfrMOHY+erSbWA5j6N/ZjZcq9WdAYEeMVMSoiDvEy5TqllJQX314hbSOhWNbBdVYCMGpx83n/NOPwnEsohE7MEER2GFdT5F1fXxfs3Lddu58eCXeMFPIyGS6kKEcieHtSYPlQVZ+LGLTu6u/YPLcE1XDEqkGBzP0DwsBz9+LvmS2pKVpyBA6F52ktWHJ9Oay2/hKc+yMqUVd4ATBeAUQs9uQokyJHqFpqbyTSufVouXjUQF58gkIAb1Jl3zZ9HycMQTCIpP1idckOO3DF2CP0Q50X5CW5ITLTqIyVuqUhsCROJls6XkzU56ILbngjKO4/lOXUlkxuoPe9RRPvvR6Lvwyl6zoa9QbKWt9mCOFoLE2XvJcSREIiZraxF5Pgvp29dPV2s1d37+fX93wf9z4sVv4zXfvp797MBe3Hwx83f3lJ0iTGWOG8hp0rqHPx888hbhTbGaO2TbXnH4i1fEo2WH5P9oEfSAA+rJLULp8DpAUioX1XwGG9h2PCeekExDprMplTBs8XxWN12nXL5idjn/Xmbzjmx9k4VuX0HjEtL0vzDcMaVtYEZtz//oyZi9qKbtNRcIZNQz2cGZ4K0uZy4944dUt9A9kxmyrGGgTQ43bDYSlqEfBkoKmujhOGSExa1YDU6btXQ00ozV//NHDdLX2BCVltGHz2p388pt34WV9fKURAtJZr3yP9klKPq/BGArCQQrBgqZ6fvS+5Vx8zEJm1tVwwqxpfP0d5/Pek5aitMHzh1cyNoXQ5fbUZWgTG9VsJFAkrKECqKEPYl8RFJx3SgeZonk0gfYwnOlL53LkmUcx0J/mtk/dzK4NrXvtI7Aci+PfeTonvecsZi9oLuvAi0aCRiyTEdu2ECIoxGcJgS0lL67eVhLuOpLG+iqklLiuwokHQsb1FPGIHbbGLINtSZpy2dbeMI1BSnj7+8/g5/9855j7W7YkVhkjNVBcydVoQzbjsfaFTRx35qLCSNIzmCUWtbAncYMnGBIIeYSg8J1IIZhVX8sXLzirZD9fFe83/J75uoYVnd/nxOYPUW4gEoAUqcLv45EmNKnuYtpVgb8BUxLe6noaPUopDYALvvwuIhUxrLxdN5fdmGgoXw0yWhnn3L+6hFnzmss27XBsSV11bFyk/KGINcLM5NjWHlVi25IsP/9YILB9501LxgzZaUNKcSzJlLp40fcNMGfRVCpr4qPuZzsWlfWVKKXLZmF7WZ+dm3cH5pPcgKWUpmcgOx6tCA5ZRgoHCGbzUggsOXaHt5HjkucV/92fbmZ3aukoSY8+KZVrFzAOSXIwyQTEQNJFCPD9Ed+ugIw7tmpcP7uJD/zXFzj5L89l/llHc9L7zuFDt36R0z58IdIeas4hbQs75nDZ166mtiZWdtCTUlBXHcOe5DPe4WYm2xacety8MQeWxUdMY9GcIVPd8CZCGVcF/XhDyhK1JU11iaLnUUrBuz55Lk7ULphQhRQIKWie28ipy5dx0cfPo7qxqmwkseVY1DcFRROVbwqbpDIeg5nJGTygylRaHS4Yxhq0haCo/phSmiEPqaE5fhenzvgADfHVgECboWMpHWNX+r0oE5gNBWJchPSkMTFlPIXnqYJdcDhK6VKhUYZ4TQXL3vuWwt/P/ephXrztsaEKmSLoAfHe//g4i5fNxxal8lcIqKuO5eL3JzeOYyGygZlJCsHpx83njodWkMmWCmsBTKmrIusHsfcg8JRCGwutDTvae6ipiDJvZsOk1cr2RNSWNNYl6BxWt2n+0TP49D+9i8fvWUH79m5qW2pZfPpCahoqSLsKrQ1HnrGI1nVtqBFampCCI08Jcip8rXFy801joHcgG5j9JtGtULq4U6TMlZLZ2+cxqB4w9LfnDx1vVtXPmVb5W+xhORDGSDxdQ9qbRuvgu/HkuYWCDfm2o/s7Z5o0AmIgF7mkypiRXL9YhRa5/xlAEMyMRu412NnHC//z5+K8B2PQrs/6+15kyclHlHyOEFBTGSURPXwzpfcFKQQRxyKbczLHYw7vOO9Yfnf/S/gjsnpt2+K4o2ahlEZpWXj4n3llM7++6zm00RgNtdVxrvvoBcybOeXNuKQJT8yxmFKboLM3VQjImDK1hovedzpGG1KeYjDponOOVYD6aXWcfPkyXrjzpUK/cCfqcO77z0DmM6u1wQgDuVmt5ysGUtkg92ISPOvaBM7ovEB4I6VyhvsfBBTygiwxyPSq/8MSxT1hpND4JsrK3d9FCMHw5oH2OORAwCQxMQXFxRSUExCCorAyQZAs5+Y0jqwfZFePvN1bX9hQNrJJK83qh1aWPY/KRITK+OGdKb2vDM/MtW3BacfOZ/b0hkKhPghmQkcfMZ3Z04NB3/VyWext3fzi90+Tyrhksj5Zz6eja4D/9727GRwlJyUE4hGLKbXxgi3cGBP8A+KORX11jKxI0WO3kxFBM6fZS2Zy+Zcv47QPn8hpf3s0F3zxTJrnNJJxh/xAI6ON+5PupMmNyBeitKR8w3XUvKJeHQY/N1BUOJvRunykoyN2Y+Ud08M+dzxyIGCSaBADKbeQJT1ybNbGDAkNYXC9YjXRmCCBRWlwHIkwolBEa7TSArJM+EA8blMzSSOWxsKxJXYus1ogiEVtPv7et/DDXz/KltbdhXyVVeu38/zKTSycPRVfKZSRPPLMOvwyUU9KaR574XXefvbRB/+CDhEqojYmXwFWDxUIUEbxiPkjr1esQ2ChUTS6s1gy8BZerXuMXc1bsbBQKBpUC2dkLsFXEWxLoJXBskXhHVPa0Jd0mVIde9Ou81BhpP/BV/lxyJCwt2PJ8h38DBbaREu0lpG9V94oh70G4SmN6wZx2uUSqrTSgSotTJA0N8rs3hhwXV1QseecciS6zPHsiM2Jl51ctCwasaivOvzKd48HxgRmjzwRR/Ly6m3s6Ogp3It8Mtb/3vUs/YPpYLbqG3Z19ZeNOs66Pjt39R2cCzhEMSaoANtQEytyQD+uH+J1sx4lFL5w0ULRGdnGk7W/ZVdkK1oovNzyLmsnz8TuK4RiKq1LnNnJtEsmjDDbIyP9D3nNa17ND5hbc3PZDOrg/VBUR1cioMgpPV5RxuMmIDZv3sxVV13FRRddxFVXXcWWLVtKtvnBD37AJZdcwmWXXcY73/lOHn/88cK66667jrPPPpvly5ezfPlyfvjDH47LeaUzfhCGZ8CU0XZ9FXwJeeGQsTrpqHiMjorHyFilbS89XyOAeE2Cc/56OXbUCaKYgEg8wpQ5TZz7sQsL2zuRQGUPC5mNTlDhNRcFJgRPvvQ6XplBRSnNXQ+9TFtnL+msx8yp9WXV+VjEZt6M0AexJ4yByrhDbVUUIQW+8VhnVqEojkDSQpG2BtBCjViu2WXtIGkGg7/LvF/GQN+gG9ZT3ANadVLn/IKW2D9R6/wepQZJ2JtoTvwRS2bK7iNEkEF9VP31OHZqqA2EmIAmphtuuIGrr76a5cuXc8cdd3D99dfzy1/+smibpUuX8uEPf5h4PM66det4//vfzxNPPEEsFqigH/vYx3j/+98/XqeENoZkLiLGlDEvbV+1lUd+cj8dG9qomd7Agn+Ik567OqclGNqqHmKmdx4NnF3Yp9CsxpaccPkpHH36Il6681mS3YMsOHURSy84jkjOcefYkobq8qGuIUMIIYhFrEIHs+wY9ZVe29LBxm27sCyLt5y8ENuWRUX+pBBEow5nnjjvgJ/34YAxkIgGmsSW3n7EPk72JRYpkkAtBpMLNS5+3jOuRyrrkIhMCov2PmObl6njMxBRSOFSZT9CQ9PP6EhegBB7Dhc2CBpij5PhHUDOST5OY864iJmuri7WrFnDpZdeCsCll17KmjVr6O7uLtrurLPOIh4PEnMWLVqEMYbe3t7xOIWyZD2NyoWv6hGhra89sYZffOIHvP7UWgZ29dJnvc5AywqM8EEoEBojfHY4D5N0tpccuyLncG6Y1cgFf3Upl1//Ho658HjIlY1wbMmUmvikz3XYW6KRoQJ+JyyeOeYDrrTB9XwefXY9F555NM1TqrFk4CBcNK+Z6z/1Nixr8tS22l+0MsQdm1k1DYh9HBIMiiY70Nby/qKSbQz0DWQpnaKFYDRV+stIkUbmopQskcGW/TTEn2JvVC8pPCLWULl8S5TtVvCGGBeR3tbWRnNzc+GltCyLpqYm2traqK+vL7vPH/7wB2bNmsXUqUP9hX/+859z2223MXPmTP7mb/6G+fPnv+FzEoJh5Y6Lcx+MMdz5T7/BG1YOufGdGlnGTaDxaK94lPm9fwkE/aUrE5Fg4C8zW9I6iLqZUhsPNYd9QApBxLbIeoqLzzqaPz//WlG56nJ4vmLF2u1c97G3kcpkqamMURELAgF8Xw1lvYeMST5GoyIS5eyKM/lz8jH84UXfjE21rqNfdqOGqRi2sTlKHE/cHgpl1QrKyeasp0hlfCpik6/u2FhYrAVKHdBSaOL2TrSx9igjjLFJ+scVpvu2PX5h9G/KG/Tcc8/x3e9+l1tuuaWw7POf/zyNjY1IKfnDH/7ARz/6UR588MF9mgk2DCtLnPUUSd8QS0QxxhQVdOtt7yHdlyra16qEMnltIKA/tp5U/Rrm2qeQiDuF2a1jyZLyBZYQtExJUDVKx7g3k8bG8mVBJgrVnmIg6dLQUMk//NUl/L9v31Gi+Y2kpz9FXV0FdVSQiFrEchV4rVy2+kRkot2HyGC2MKC8q/YSrO0Ofx54FB8fgUAJTY/VWbRPlBgnOqdxUuR0KuJDrV8dW5aUGS9gCeobKifUxOnNvhfGjaC7R/s+DEIEyaACgxBDQTR5bVubKCl9PImaE4nkgj0SMXvUjpX7yrgIiJaWFjo6OlBKYVkWSil27dpFS0tpBdOXX36ZL37xi9x8883MmzdkJ25uHqqRfvnll/PNb36T9vZ2pk+fvtfn0dU1WBhQUlmf7r7AuaNNEL6aJ51VJRFIPQ8JqpcZrASlCMPGyO+YkTmegWGCxpICe1hGtGVDQ3Wcgf40mZRb5kBvHo2NVXR2jtbac+IwkHLxfM3U+mrmTp/CltbdY1Z3jUUddnX249gWg7ZFRSx4pIWAbNqdUIMRTMz7MJB2CwEcSmtOsk7h2MoTWT+4lTvNr8vOYGt0PSoL27OtTHObC8Yj25LERkkEFQKk0cQniGY3Ie6FmUOdKV8WQ4ggUdfXku70MWT9enrSi2hIrKSxYgXaJOhV72Rz1+XUVg05slVllOxejj9SiqKJdcn6fb6gMjQ0NLB48WLuvvtuAO6++24WL15cYl5auXIln//85/ne977H0UcXx6h3dHQUfn/88ceRUhYJjX1BiOJGMiMf1nh1glnHzUVYQ3el64+CbNvoDb4NmqToKFqWbywOgVpdXxXHseQeZ70hoxMd1lDpcx88h3kzG7FzfazLsbtnkK9+70529wzgK1XIRDWGsjkSIWNjcpnQEdtmu7121O12iZ08Lx/jDvnfPOI/UKiDZTCjRuwZA/1Jb1IX8itBOHSr/4c20cJ3PxJbesSsLla0f4FtfZfwctvf8cS223mh49d0ee/HEk7hG8+X2Bi30zPjVOFs48aNXHfddfT391NdXc2NN97IvHnzuPbaa/nsZz/LkiVLuOKKK2htbS0a+G+66SYWLVrEhz70Ibq6uhBCUFlZyZe+9CWOO+64fTqHggYhoH13qlCuwfc1/ohBu6+jl59++Huk+1N4GRcnFiE23eLI3wyCKP1KpHE4Pftl4qahaLnjSKJOUJnVGWZuikWsCVUTaELMlvYKQ1/SQ+XvndZs29lL++4+Hn5mHRu3dZbdK+JY/P0nLmFaYzVOTquzbUl1YmIlJ07E+zBcg/CVLkST/WLgFlrVjj3ub+NwrnwbR8jFSCFIxO1RJ1pSCJobKooKNb5ZTJR70ZfMglrP1Ni/EJfrywpQY2BVx6fY1ncJAJUxJ2hTXBMnk/FI5CInLSloqI6yt3HFe9Igxk1ATATyAsLzNbt6UoXaKFlPlcRoa2PIpD02PLGG3Vs6qJ8xhYVnH8OKyh/TLV8vFhJGUGmmclr2SyWfGYtZNNUlSqKVoo4cajo+AZgoL8Pe4HqqqPFMKuPj+opHnl3HnQ+tGHW/M09cwFWXnERFdKg3RE1FdEL1iZiI9yFfaQCCPJ+89v2n1P085z67V8doYQbvtN+HEFARc8aMV6pMRGisGb3xzcFiotyL3f0ZtDbE5Spmxj8/at6D0hEe3/pdku6soCqDENTVxPFdv+B/iDqSmn3wPxwUE9NEYyhNPV9npsxGBizb4si3LuHMD53PUecfh4yAwqMQrJf7IXE4JvvBkkNEo5KaikjZUNbDRuq+CUQcWeTbiUaDEFgpy3XWGGL1hp0MDHoMZlySaQ9PGTx/cpadfqPoYU/uKbHT9jrsNZuPxBkl1HU46Yw3aWo07Ymg41zwjWX0MQx6i4vKeA9HCMWM6j9hUVw2fLhJaWT3wP3lsBMQQlCU2m8K/yumXAOUVvspBmTrkHYm8sdQaF8WHSaRsKirCvonl/M5vNmzo0MbUeTItIQg6tictHTOmK1fY1EHTVA3y9eGVMaje9DFU+Fg9EaollW823k/UcaekUpjMUcsAIJXbU/PvtKGVDYU3EChJSkE/p81Xf+MqxrLbiuFImL1YzlDY5EQFEVSjlcNpsJnjuvRJgDGUCgfHSwQJfJBiKBw30h2WM+iRfnY+93OSrQJajpVVtjUVEQLzrhyCUCHkeXuTcGxJc6IGk3Tp9Zx5omlZdSD7S1OOW5+kKw1TGC7bhA6m3b9MFFrHzFAizWdT0S/wF8613KZ9S5axHTsYcGPwkgiRDnOGlZ/rIwPbySpjB86qylO4FVao3HYOfgXKF0qlI0BXxcn3w43YwsRlPkeTyZGvNk4s6fBWY+S8qkpP6sxGDRB85SqSpuKeKRo/3KfF8qH/ScesfA9FVTPzZXj+IsLjqcyEeG+x1aTT1O0LMmR81s4/ujZQDAry6fPGHLl212FUoZEzH7D5ZgnA0XfzLBnuF5OoV5OYZaZy3rnFZ5PPY9nfGaZ+RxnTiUhEkPPfGn+aAm+r/CUnvS9q4f3PdEmGDc6Um9nWuUfEGIXcpiwFQLm1N1DS/WzeGoKHam3YdnvJK+MSSHGvUHTYScgRrb7KzubKaNVADR5x7I18khQbmMYEotGs5jaqgjxWOlXVk4YhBrE/mNbMmgolDMZxqM2UdvirJMWcezi2azesBPX85k3q5GWxtrCfr4yRIYl7CplwAqK/SXTPomYPeHyI95UhnXEKgpRLfMV2cLmjIqzOZ6TsW2LgVQ2MBcNe9w1sCdLeFAuRWNHJ6+AGFlhOj9mKFPBqs5/5cSpH2LkTDbIsN5F3N5FhbMJVzzJFm4CZM7/ML7P9eF5d0b0c9gbhIDp7tlETQ3CDBcCEonNjvif6JOby1aELfcZYSrE+BCP2QVThBCCSEQGBebiUU5aOpczTjyiSDhA6f3wfD2Ueao1yYw3ZvLdZGO0IUUASTPIZvU6HbqtaNITaHVBlFhdday4B8pefrXp7OQ2Mxlj8IY1MBtubopYPSg9diUAS2aIihVUWM8H+xyA0OHDToMo7xEYQRmtQhuwTZwTBj9PW+QZOuwXSFkdIAy+SNPGKnapdZwg3s1i6+zifcPB5oARmJbsQmy+EIKYY5Es4+QUYshJanJ2DkkgFHxlClqD0YZkxqMi5oSaBPlOZCb3e7DMGMN96XtZ4b6ChY1BUymquNy5ilqKyw3EbIvqRISBpEc66+21gMi4/qT2CgUmpWE+iGG/u6oBuReVXAVpquw/k9KnjLv/AQ5LDWLPnRdGz5YGmxgz3bdii2hOkAy7gXi85N+Ob9yS/cp/zmR+/MePiGMNG7jAsmUhGU7Ibix7C0J4+MqQTvsMpl2SKY9U2iPjBv1ARmoMRhvS2dBxDZT1yTybfYZV7koUCpcsHh69poffuf+DMaUteG0pmFITo64qWr6mWRlGizCcLGhd7AsdPtHM+M30pheh9J6MdRJt4rmWp6GA2COWLI6h31ekhERC0G9tK78eSafe9IaPH7LvWFIUMkXzMjcW66NuyueYMvVd1DV+jIapl+FEf4ewOrHsdiAIH/R8Qyrtk8x4JcJAKU06qya9IB8+rORlxbPZp/EojugzGFIk2e5tI0WKlC4ueAlQlYjQWJcgEXX2znw0iRU4NaxUjwCMKn4OX2z7O/qzC/B1FF9HR5nYOvT5F+UmTOP/ZR52JiZjDPGoXRzqOoKyhbGAWNSiMm5jWyA8iaH0GAaDzZAHVBvNoOlE6woqZO04XEFIOSIRC0vmi5oZopV/hZDbEMJH5EKTGxq/S735PmBjdD0DvX+P7x6PATJZn5RtEcsdJ4/nqUKE1GRleG5J/t1ImdLBH4JEut/2/4akTgLQZDXzjsRyZhEU5jQGIlJSXR8n40boG3RJu17ZwS1iWQjEpNXi1DCBYKBotBECfFXLk9u+TWVkK5VOB7PrH6Q+9iJSZDFIwCZlfYisXkj1OCfI5TnsBAQE0S4DabfQLGhPOBFJ1Yj6MdPFUlrNCgzFXmmbCA1yLgBbvBd51r0VhYtJaxqsWZxf+XGqrLDd5XgjECTiwaxUWCsQsq2k25YQQXlkUCDbqKn/Ij2dt2B0A4jd+GoaqWwliWhxFFPW9XFsMW5tGg81hpuYpAiEcKNsokO3l2yr8OnX/YW/29RO/mvw53wp8QUSOd+EyLVKiToWzfVx0m6E/kEX11e5ApcGS0pqKiOTWnsbXh8u6Hg57LsYdk8G3dko5rG+50wqnXU0xJ/AkhHSXEhV7TEIkcQ6AOYlOEwFhCUFdZUxuvszaFXmATQCSwaz0ljUJhax0NoUta48wbqKHn8brkjimQwWDgLJWc7HkULSoV7nSfcXKIb8EZ1qM3/o/yZX196IJey9CQcP2QeijkU0YpFW29gr47Vwqa7/Oyy7Lbd9oGlkTTOO/hQOywubpjKKyoSYlL3D82NRRmd4MfUyr6c3UStr2aU79mp27xvFi+mXOKvyzJJ1xkDMsYjXJ9BG4/s6CAix5KQOEAiE6NDks8J6hDmNPyFmt5NVTWzr/wDJ9NloZbBlUEkAIOnNx5aDVEQtvJzWJoQY9wzqPIelgICgmmpTfZxkyqcvlQWCISJiS6JOIBAsKcjqNP2qn4SoY7hLJiaquNi+nr6KdWzrX0+FaGCWPIkKKyhstcq9p0g4BMc3eCbDVu8V5kWWTcKh5sATj9j0peayN6JXCI1lby01KYoOfPFN0EkcczUQRDplXDVhehUcTIQQ9Kl+/qPzh2R0psT3kMfGwS+zzsej1ds55mcEjm0x7rWCDmX83OS1xr6LqbHvIEUwTsXtVhbUfhuLLl7vujzocSKgIfY4R9TdBIhcrwjNgLqeiH3OARtrDuu3wZaSqoRNNJIf+INwPq0Ng9k0T2V+zRb/BSQWBsMi61yOFpcgcmEYlrBZEDuF+tQxhWPmi2T1mVL1G8AnS6/qKNo2ZPywLUHUOR5PzQBr85hN3fPVfMsiMvjyZmx1JSLnU3JdRcSWk87UJITh7r57GNSDY2oMKtdhbuQ2NjZNdtOBPs3DCq3zOrBPU/SHBeGQx5JZ5tT+il3py9FIYtYOFtb9C5Ys3q5af52MPRdYeEDO87AWEAAIMcy3kI/1FjyZ/Tk71Co0fqHExnr1MFI6HGVdPPrhcj9rRAtJ012y3iZKrTW1ZHnIeCFIOA4DqR+iItcj7ecJ8naDEsn7IpMNHhl+jJTrEDRh63eTzi6mMi6YTMZBIQRrMuv2aE4KmgFJSrJ7kZyUWDbseAfiLA8vtAmquNpiN1KU7/4mhcfSxr8i5c8BwyiTIY8q6zek+coBOc9xmypt3ryZq666iosuuoirrrqKLVu2lGyjlOJrX/sa559/PhdccAG33377Xq3bH8o9q0ndyw61Mlfae9j54bJe/wldLl06R7441tLIJVgUN6MRSCIizmzn2HGviRIyhGUJYtEGTOa7ZPvvJdt/K32dt6D8uRgTwWhnbO2hQBZj/RItH0eJ35O1PkhW/w5vL4MbDhf2xe8y35pPlVWFk/uvRtTywZoPUGUN9RQINec9ky8oqU0llImWBBD4VEY2MSX+CFMSjyJF6XYChU3bATvPcdMgbrjhBq6++mqWL1/OHXfcwfXXX88vf/nLom3uuusutm3bxgMPPEBvby+XX345p512GjNmzBhz3f5Q7mEdUJ1IHFSZ4nwKH58MEUqbUzvDIgWarPmcGfkwz3m34pkMGk2TPZdzK67FEnb4khxAbEsGUU1Rm4FUNYZqlGqmb/ePiMQfQsodxCt/jxDlQzUh31rTIPKqvdBABk9+k7R7AbZdN6kc1ovjC1mdHluLcHA4LX46S6YcyetdW5FI6mUD0WjxMDJ5vrU3jjL5jP9KBv3TqbSfQg6rJD18giNzCbvlJj2GKJ5YxoFiXDSIrq4u1qxZw6WXXgrApZdeypo1a+juLjbB3HvvvVx55ZVIKamvr+f888/nvvvu2+O6/WWkSbnKakSP4oizcLApXwNlZIe42c7xvCt+I1dUfZX31/4by6uvo8rKtSQN35IDhmWJQu/dRCzoxxtP3E1982VUVP/HXggHCIRDubU2vnkKb5I1tPmLhstIyDjOKHNGB4fFzlHMtGYhhaTRaqJCVrJbd+KaYrt4ODnaM8PDe9sy15HyF6J0DF/Hx9R+h/etNkaCSJAV7zxg5zkuGkRbWxvNzc1YuRrLlmXR1NREW1sb9fX1RdtNmzat8HdLSwvt7e17XLe/DK81A1Aha5nlHMs2r9jMZBPhaOdCorZdMkBEHFn2wRdCUmM3lawLTUwHDoHAti08L3Aqq9gGTPTbCJFFMDRYjfai5eP0x/qErKtzxc8mx41sjNTzN02f49nk82zKbqZa1lBDHdv9bdjCZmnkWObbCxBC4Bufe1J3scpdiYWFHtAsS5zIZTVvxxIWe1Xve5JickEynq/wcq2QDTFeHfweQq0l4Wzj6KZ/Q1A6QVEmRlYvIm6tQWBIqlOpnPJ1TG/NATvfw8pJPVpvVc9XJQP+lfWf4+62H7E++SxSBFFMJ1ZdzGk1VyCERGlTyHSc2lw9asy2EIJ4tPRrjDjWAYtNfqM0Nla92aew3+SvIZP1CwX8ulO/J+WV0wglWscRIlkiKEaboQmhmFJ3HlIkSMQdos74h2VOxPvgK008FWNm4yVA4EQdSJZ3nt7e+VtWe6+icv8BvJh+iUQ8wnunXUFVReSQyXE40PfCGIOvDEppfB38BFDCpWJY0ap01sVSPo6M0u8uozryYonPQQibgciPSVqB7zMasZBOjMbyDejGhXEREC0tLXR0dKCUwrIslFLs2rWLlpaWku127tzJ0qVLgWKtYax1e0tX12DZyqpaa7JeqUQ+1foASxPvImOCPAhbRejuThdt09BQQVdXctTPdGxB0iodRKKOhZxAL8lEadC+Pwy/BmMMAyk36CAot4Msvb9CaLKZOUSim8uanIyRQAQhMhhjIbCx9f+jp1sAg/Q7VqEG1IG4homFYSBVXBIj4/olE6usyfJi8iV8U+y/84zHY11Pc07kHLxM+YnaRONA3QtjTND2Vml8pcpqq+msTzITfIdRawdH1PwNtgzOReBjjI1vHGyZQWkHg8XGvhtIqhSxSDawXFREqauK7dc1SClGnVjDOPkgGhoaWLx4MXfffTcAd999N4sXLy4yLwFcfPHF3H777Wit6e7u5sEHH+Siiy7a47r9ZTSbqCUFERGnWjZji0jZbfaEHKV05UQSDocjQggiudm9NCeBKW3RqHWc5MC5lMu6NiZKNvVedOYzaPdstPtO/NQvsM2lhW18X02ivhGl2bhOGQ24X/djjdIOSArJIKNPpg53lNZkXUUq65POenh+eeEgxPDGZpqFtV8kanViyzS2TGNJDzB0p46ntf8iNve8l5fafs6gvwytIeMqwBCxD/wYM27To69+9atcd9113HzzzVRXV3PjjTcCcO211/LZz36WJUuWsHz5clasWMGFF14IwKc//WlmzpwJMOa6/UXkWvGNfNellAh0yfDhGxePDDHGngkJyguCUDYcHBzbIusqbHMlPreC8XLRSGCMhdFVZNJvp7N9Jo1TrwcIopZMDN9bSHrgI4hYAimuJOiDJlA2Q+1KTTALtOTkyP61LIE3TDGQUmBZoqioXLWsLpiVRmKMoc4+cPbwiYqvNJ6vi9qH7ol8JH2lsxpb9CFG9KixpEttfDV/3vIbpICqikhB2GgdjGkHIxhAmMOoWtZoJiYI/BB+mbpM+ZsL4JkMz7q3ssV/EYAICd5afzVN2ePLHtOxZVk/g21NvJICE9e0sfeUu4Zkxgvq+9CGJ7+FFo9hECjvHLLJz5DN1uK6PhFngGjiQYQcxHePxXePBwQVlauIJP4d5GtABKHeQYwvIIgDQb/ryrhTejLjeA0TBaWDlqxFy5QOWooO4xH1J54beKGo7IaDw6kVJ/OupssKvTomOvtzL/K+hXwBwr3ZXhuTEwyC3pSL6ynqY4+zoPYmbFlqAtXG4qFN9xCPWsSjQ8VEBVBbGaG6MkJzU80BNTEdVk7qsZBSBMHHI7CkKDzmD2d+QKfeVMisztDPgz23cGbkI8yyjyu776ifFXJQiDoWvq+RtBDV/4YxhsGMj9GGiIRIPIOp/S5O9B7AQ6tpKG8RILCctUQqP4cQmdzRshjrDrLmdaL6FgQCrTVK60lRfsOSAiEpaqtrWRLHkXjDfHjLGy7DdzUvZ19CiKD0xqmJk3lb9UWTIovaV4bWth42bdpFTU2CBQuaS2bzwwWCrw1K68IAL6XA8xS+r+hLL0DUlg+5H3TnYkmIRYorTVtSYFlyr9sp7w+TR0CM8uQGtmxJR3Y7u/XmgnDI4xuXl90/lAgIxy4f9po/ZsjBwbaCBlF+TgvM+yayuVmvlfhbhP0KIlfOwLJ3UFn7FQZ6biJWcSv5Eh15hHAxrMOwCsFSjAkau0ywgLQDhMCRElcXm0qijhUMdDkTiiUsltdewqXiIgb0INVWFY4ISrEfznJUG00qrfjxTx7ipZe25AZpQ1VVnC984e00NVXnKtaCN4pzOo/n+Tz2yGpeemETyruak4/dxoff9TwtTYMAKB1lQ9e1JKKl2ms0Yh20IOLD+HYWI4QYtWa6JSX97ESO4nwbMJ0jth+9vK4lxajCKOTAMLLZTzTf20FuKBIOeYTMkqj6IXZk3SgzXoUWawp/lTNNHq5YZcxDgqChUixqE4lYVCYcLEsSkREa7HocEQxiQowetHEoY0zQCiCV9rnzrhd5+eUteJ4ik/HIZn26ugb41rfvJZ31SWUU7gjndCqVZdu23Qz0p/MH5Fe3PMITf15Df1+KZMri0Wfm8sl/uJy2zhp60kfw3I6vkzYn4DjF36cQQQj9wXoiJ40GAcHgrUZ52evsplHLDCREseNtrPyG0Lx08LGkxHGCxLkAQSxqkdbPAeVj+S1nE1rNANlXZq2NYKg66WjPzOGInctSHzn7FUIUSs2MZm6zy4R7H+oorcl6qvAMPPTQatwR3SqNgcGBNK+/3sHcecOfG83vf/ssTz+1AcuSKK056qgZnHnWInbs6C5ovfljpDJR/v1/vsQ5Fx9PLGJRHbNL7oNlydw9OjgNrg4/cT8GY83sm+x5VMkpuWqVQ9giwhLn7YW/95TfEGoPbw5RxyrSBiwpsJyXRt9BV2HcD2FMcVmV4IWMIs1Zw5bpSdP5LOjZ8MaGBfsAdTV7s3B9TTrjF00QUqls2W2FEPT3Fzua//D753nyifUopXFdH+VrXl21jVt++gieW1oHTmvD5o0dVCUcbEuUna7GHQtjyocgHwgmlYAYy8wkhODS6r+hyZqHhYNDDAuHk6ouY4F9BpYlgszFsYSDDDWINwtLCmIjk9rk5rImJGNAq6Mw3kXo7HtzFWArMCYBZipkf4QxFkrrQpSb6wfOam30sBj2w5M3UgEgXxvrcMBgSGcVWdcvGaSnT68vu4/va2bNCloNK63JZnyeeGxdiQZgDAX/WDniiQham5K6bxCMLZGc/8E+CDkQMMlMTBA0EVKqfBx3QtZwec3fMaB2k9L91MqpTJ0yha7u5F5pBhOttMZkI2JbeLYeclibOozYUWZLC9TpgEBn34/RLSB34Lsn4nsnEXdsslaxo9b1fJQaur9SiiBPIOdzOpwCE6zcte1N+GaesYI2DiWMMaRdv6xZ0RjDO995Mjff/MAwcyY4jsWxx82mujZB1lX4WrNjR9c+a52OY3Hq6YsAsMt8lzFHIkXwnB8sX8+kG9HyL/VYVFlTaHbmEbUSWJbca7NRaF5684lH7YLWYJv3g4mX2cpBe+cjnDuxq9+OFfsOVuT/iFZ9ETtyB6LM8zHyXdfa4PtB5mw6m3dMHh6ahRCixPG/Jw4H/4M2Qc5HOeGgtCbtKuYuaObaj5/PjBn1SCmorIxxwUVLufKq08nkhAOAmxldSxiJlALblhx34jyOXjoLaQnkCEuHEBCNBm0EDmaeyaTTICCY6StdXot4oxwuM6hDHSkE8ZhDKu1hmQvRZiWK2wm6zgUx+yp1I4hOrPi/BpnVw25btPI7iMxS0IuKjjt2tzWD7wcCw84lTx7qk4V8rL3ai+xgKcUh739QuZ7k5bQmlavlll+3cFELf/vldxTWuZ7GHzE5aNiHIoDzjpjK2y49kbr6IGEtYpWOJY4tsaUkFrEO6jgzKQVEuRIC+8vhYn89HHAsSSxqk8n6RPQX0bwPLZ5DUIHvn45SDiLyL1C2J4gH9m/B/fuhJdrnz10reWJgLQJ4a+0xnFe3BEeWvj6+H5i4Io48pGfVQghijiS5FwIiuo/axkRDm1LhsH17F3fc8SKbN++iuibBeecv4bjj5xTtl49wGqk4+r7if3/1eDDx2MMQ4zgW556/dEg42FZZ/0MiahN1rIOesDkpBQTktIhRfBH7ymi9IkLePKKOhdIGz1NIpiHN5UBQZ8mJadJiN0KUrwCL2BUkPClwtc+3dv2WNr8bL1eDaHtHF4/3ruWGuVcSkeXLcLieRmlDxD64M77xxLIk0UhQ72o0HEcetIiaA0HeIT1cOGzc2MG3vnUvnudjDPT1pbn1v5+gvb2Xi992XLCfMbieLpsMt/LlLbS19ZQVDkKIginScSyOO3EeU6fVAYFwsMuYjyKOpCIWeVNKmExaASGFIBqRZN396xxmWwcnHjlk34lHraBmzoiS1b4GKU4F8xyI4kxqY2L47sn4uefiseSrbPc7i9511/hszXbyVPcGTq1elHsGSh3VShmyRuVCcA9NIRGxJdqYolIbeYSE2AHol3EwyWRLzUr/8z9P444IQ3VdnwcfWMXZb1lMIhFF+WbUaLZXXt6CN4pQnTeviWjUIRKzOfrYOcyb3wwEhSfLCQchoK4ySsR5c8aYSSsgIMj6dGzzhpvUC8LIpYmMQJCI2aQyfkFIaJNv2nIpOL8EdoMIBoOgAmw1fmaoac6d/c+UtRJkjcfzgxs4uXIhrjYIIYhGREl0idaGjKsOuu14vMg7rKUQuMPMKbYliUUPbc0566mSCqxaG7Zs6Sy7vW1Ltmzu5KijZ+Dp0SeWo00YhYCpLbVcedVpGKB3IJNLQJRYo4wjVYkoFXHnoNRdKsekH91syxo1N2JPRA7hmeFkIS8knNxMd2i2mID0L8G/BEwlxlSi3LeT7f8FUAHAa+6OUUtbA0SHmZeMMWSy5Us+G2PIeuqQzZ8QCKKORSJmE4/Zwc/owQu1PBAYTFnTmRAUnpWR+P7Q9mMFISw5bnbZYziOzbKT5xf2d2wr8CuUEQ6CICKvpuLNEw4wyTWIPBHbwhdqrzUJKQOV8FCPVJksCASJqEVagJsePoDXg/sP4P4DnqdwlZ/rqRyw2+9HjOFpPKvq6KK/+/wkd3Y+x4vJ13Gkzbl1x3BZw0lEpI3WQT2fQxlLBtXKDoeJkedpomVGXiEEp512BE899VqpadLX/OKWR/nYJ85n/oJmpC/wdS7LXkBbaw+//c0ztLf1oI0plCzJC51TTj2CuXODUhxRW6JiNm4Z052UgQ+tKhF50y0UoYDIYVsWQuiyN2w4lhWohIf6CzL5EMQjwUA9qLyCo9DVPv/X8wSPD67BMz5NVi1X1JzJUdFZtDj1WIiyOkS1SDDXmYrBIBAMqjTX77iVAZVGoUHB7zqf5aWBzfzj3PcihSg0qw95czHG4I0RnXXFu05iy5bd7NjRVeKfcF2fW376MP/4z+/BcSS2ESCgtzvJj2/+E9nssMg4EZillp00n1NOC4SDZQkitsSSkhg2rldcK8yxJJGILGhsbzb7LZ7S6TSf+9znuOCCC7j44ot55JFHym734IMP8s53vpNLL72USy65hFtuuaWw7ne/+x3Lli1j+fLlLF++nE9/+tP7e1pvCEtK4lGbiCOLwlalCHpPRyPWIR2VEhIEFVQmHKKORAj4j11389jAalwTlFXoUL38pPs+Xsu2Mj86lSanDmtkfS4srmm4AKUCs9JOt5ubO/5Iv0oFwiGHa3y2ZTt5ZXDz0DJv8tR1mqhoY8bMEo/HI3z+by8ZtWyO0oaNr7cDuc5uCB5/fF2RCQry2oNgaksdCxY0E4vYxCN2wUfhWLLwGVIGVYkjEQtbSqoSkYNW0nss9ltE/exnP6OyspI//elPbNmyhfe973088MADVFRUFG3X2NjID3/4Q5qbmxkYGOCd73wnS5cuZdmyZQCcfvrpfO9739vf0xkXLCkL9f8TMYdk5M2X5CHjgxQCgSEasWlXu9iQ3VkIX83j4XPX4DN8pfYqPt94Ob/qfphXM1sCU5WM8u7as1kcC9rh/qHvKR4aeKXkGHky2mPF4BZOqJoHBMYqpc0hn1h2KDOGfxkIgldsW44qRASUVHTduqWzbFKh5ylat3cRLzOGCAEVUZuMq4IoJRFEw1VXRiaM+Xq/R74//vGP/Mu//AsAc+bM4ZhjjuGxxx7jbW97W9F2xx57bOH3qqoq5s+fT2tra0FAhIQcDIbPCjdndyFHmae1el1IARUyxiemvJ2MdskajyqZKLy8G7KtPDy4YlThAGAjqbKKy334Sr/ptuWQsYk5FguOmMpr69tK1imlmb+guWhZc3MNmzftKhEqtm0Rnxnlt20rsITFmfVzmBIJkuIsS1JXbZP1NK6rcBwr5/yfGMIBxsHEtHPnTqZPn174u6Wlhfb29jH32bhxI6+88gqnnnpqYdlzzz3H8uXLed/73sejjz66v6cVElKW4ebBBruK0fT4aiuBYCi3ISYj1FgVRS/v44OBaWospJCcXXtU0TKtR4+hD5kYCCG4+urTicWcoklFJGJzyaUnEI9Hgu0I/JIXnL8Ee0QfeoOh+ySf/21Yw8+2PctPtj7NB1/+H+7seJV41CYRDcxNiahNXXWUipg9oYQD7IUG8Rd/8Rfs3Lmz7Lqnnnpqnz9w165dfOpTn+KGG26guTmQwm9961t5+9vfTiwWY82aNVx77bX88pe/ZP78+ft07LGab+8PjftQV2Uiczhcx3hcQybr42vD2Q1H8aP2B8hm+4tqLUWlw7unn0FDQxW+r3FztuVXB7dyW/vjtGZ3M8WpGVX7AJAIbGHxmXlvZ/G0GUXrGqZUEY+UD288VDiUnyXPV6RyxfTGGjMaGir5znf+kt///gXWrNlBQ0MVl73jBJYunQXkO+gFk4gZLbV86UuX8t3v3leo9OrPlaSOyeKZYg3zx1uf4fy5i5hbWY82FHxSxlAIehhJvnqwFMHP4f6LA3kv9iggfv/734+5ftq0abS2tlJfH9RJb2tr45RTTim7bVdXF9dccw0f/ehHi0xQ+X0BjjrqKE444QRWrly5zwKiq2twn0oU7w2NjVV0dg6M6zHfDA6H6xiva9BGk8kGL+0/zLqSf976O7q8ASwh8Izi3KolnGwtpLsr1x/YaJ7ueY1beh4oOKGTahcWAgtZ5JiGwKx0etVirmw4g3q7kq7dQ+fcMKWKrt0DRCMHv67OeHE4PEuprEdtbQVduXs8GrZtceWVpwBDY1p/X4p84UejTTDIY5g+o4F/+uZ72La9CwH8IvsiGwe3lxzT14r/Wv08H55RfpzcEwKQUhKJWMycVlt4Tt8IUooxheR++yAuvvhibrvtNpYsWcKWLVtYtWoV3/rWt0q26+np4ZprruF973sfV155ZdG6jo6OgjbR2trKK6+8wic/+cn9PbWQkLIETsigBEdzpJbvLLiGLZlO+lWK6fYUEhR3mZMIftH7YIkgUBjA4AirMEt0sJgWqeeDjediC4uwhuPEZLTM9vwigUAZgzEmmNkbg9JB9JPWJpf/AOSEw3CLYVNzLVIKUpvKt7tVGAb98p3p9oYg0EGTyeiivhQHgv0WEB/5yEe47rrruOCCC5BS8vWvf53KykAiffe736WpqYn3vve9/PjHP2bLli3cdttt3HbbbQB84AMf4IorruDXv/41Dz30EFau+uUXvvAFjjrqqFE/MyRkf3EsWXjZhRDMjQcJTMYEpVeGZ0Svz7TijeJrEAjOqFrM2vQOJILTqxZzUc3x2LmEu9FCJSeYqXlSkFU+K/vakAKW1kwjEbORUuD7QZdAXxu0MkHnQB0YHfMCYjQKAkXkyp7LwPQjpODUujm8nt6NO8LEFJM2y2pm7te1CBFEWMaiNgdSlxPmMArKDk1Mo3M4XMd4X4MxQZ2kcq+Ar4aSJu/rfYn/6Xps1OP826xraHRqSpYHJb+LzUh5E1M81/zlUORQe5YMhj+1v8Y31z2MFMEMXCD4x6VvZ5HViPINrjK4yivKeQluj8gJiUBQaJMTHJA/0PA9inxZKeXy/7bcTY+fws9pnxFhMTtez78uegf2GzAxCgGOFSTR2Zbc73txwE1MISGHKvlCdOWEhG1JpATXM9RYCSQCXabkho3FFKc6iEoSQ+sdy0LKwN8xHKU0UubMEjp44Q9VQTHxCPwBShlUriijrwyvD+zmn9Y9SHZEk7C/X3E33198Bc/1beO2tpfoV1kqrQgX1i3mL+qXghEonR/yDRiR0xSCe9bpDdLh9jM1Us0Up5KRJVniMsLXZ1/CPd2v8szAFiwheUv1Ai6uX4y1j3WshAjKb8Qi9kENkQ4FRMikJi8ksl5p2WcpJLEInFp3BD/f9SBZSs1MF1WdUHB4QxDyGPQaMWUbUmVcFWRgjxistr/Wzu3f+SMbV24jEnM447ITuOLTFxBL5MMpRShMcghBwR+gcv98P+i/oU1pj4Y7d60qW33VN5qbNj7MxszugvAfVC6/272CP3av4QvTzuXIRD7fYeh7z2iP/9j5GGtS7dhC4hvNMYkWPtVyFrER/UEqrShXNZ7IVY0nFqo/J2L2XpkYhQiSdqMRO1ee4+Df+0MzjCIkZBwRQuSqao7o56A1rq+xtM3npy0ngo2DFYSwIjkhPp/ldSfT19FL59ZObEvkGsoXHyebdlG5wm/lmkvt3LyLf/v4T3ntpS0oX5MezPLob5/nXz/5czJZn6yryLg+6axPxvVxPYWvVGArP3wsxKOijcbzFVlPkcx49Axk6RnI0juYZSDlksp4uH7wfRgTZEr7vibjBT2md6T6ymp/vtFsyHSWXZfWHv/a+iDt6X58PxBG+a/6p+1PsybVhmcUae3hGcWrqZ3c0vFM2fMPZv+SykSEqgpnVL8UDLUQqIg71FREqauKBiHRb1K0Q6hBhISQFxI2vtRkPB/X1UUaxeL4TL4/92O8nNzEoM5wZGwGkXbDdz76U7rbe5GWRFqSv/jcxRx3ztFgYP0Lm7jj+/fT3daDlJLjzzuaa7/+LrIjIk/u+vEjJU3ufden9fV2NryylYXDWl1qbYIBLXeI3Tt7uOenj7L62deJJaKce+XJXPDeU7HtQ9PHkdcOfKXZluzlO68/xkt9OxDASbWz+MTM0wuZyAYwOnAuK63x/eAnUKRFLIo3sz61q+AHyJOf/Y+GMpr7utdySdUxpHCpcxJYEXgxua1kP89oXhjcSkqdQsKKFHIkIhGLSM7cOPK8hl9zoClYOJbMlWERo25/MAkFREjICCRBUT9vRARLTEY4repIANyMxz9+9rsk+9NFpufbb7qbyroqjDH88vrb8bLBwK+V4uWHVvMvrT18+nsfLBq8N63aXt5R7io2rNjOrKNn5hKkcj4LgmSprrZe/vmD/0k6mcVoQ3/XIL/7wYOseX4Tn/rXq7Fyne4sOTGrD+eFQcFM5Ck8FZiJet00n1j9fyRVtvD1Pte7jXWDu/j+onfhaAu/jDDIozVorclqxeqBthLhAGAhyy7PozC8kN7KY8kNCBEkPp5XsxB7lP0kkjQuU+IVOFJiWaMIBII8hny7VidnPnqzhUE5QgEREjKMILxVBG1ELYFW4ClVUuBtxZ/XBIP/iJfay/r8+bancdNuQTgUju0pWl/vYPPqHcxdEpSnEQiqGiro210aiWJFLKrqKwJbOwajcnEyuSqhd/70ETKpQDjkcbMe657fxOuv7mDWkdOG2bqDa5JSjDBXBL6NwnXk/BxSmMK6fGavGLZhvtfBvjEkDDyl8XJ9u0cKRyHgnl1ryGq/6OvVGNLK476ONTjC5rnBrcQth7dULeSo2NQgV0EVaxE3dz3GendXyZkI4KTK2Tw1sKmsiSm/Tb/OFCKWXKO4r2fNKFsH5z27uhYnpy4MvywpAt9UUK1VFGkJI7edSIQCIiRkGLYlcHMDrkBgWWBZNsaYYFZqggFo985u3IxX9hhdrd0k+1Jl12mt2bx2Jw1zm9AmMBnNOW4uO9aX1i9z0x5dPSnaupO5stIUBnKDYc2zG9FlHOG+p3j5ydeIT60rWScAIQW2FcxiR5YLEYjCuCUK/xtaLqTAQ9Dfl8lF9MicQKFQCiKfEyBy56k0uJ7HQ52vc3/nenytOadhPufWL8SRFi/0beeZ3i0029WcX78I21i80rezpEQFQNb4/K5rJQpdyC9YldzJqfG5vLv2xKJtO/1B1mXL14UzwOZsF7VWnG5V/l6VG7M9NFFhYyHJDsuNiUqbK6cehyOtQjCBndMSAoFgHZK5L6GACAkZhm1ZaENJNzEhcsICgYNkzsIWookI2ZRbsl3TnEY6t3eTHsiUHF9IiVURo6c/yKRN9iZ55vfPj3o+D/3sEabMbaZhZgMiN/vPD77RRJSBMmlSlm0RSUQxxpSYlvJ2e1cDqJymNCQoTJAaXIahhVlPF2oZFV9crteC0vja4CuDQaMNfL/tUdamOwqD6obkLu7tWMtuL0mfGvqeftn+HF+YcQ5NkSrWpTtKZveCQEgMX+4axdOpzZxRMZ/pTm1h+XavZ9TwZAAfxd/PuIh/b3uYDncAldtSIqi3EwyqLJkyCZJZ43PNtJP5bccKBpRLlR3lvdOO58oZx+JYVkFTK1dT6VAjFBAhISOI2EHUiOcHjmopBEbkzRcGz9fMPmE+0YoobsYrMvFYEYuT/uJkunZ0cd/ND+APNzMJiCQizFo6G4B0f5oHfnA/vjd6RVjlK1Y9uJK3XnNOwSELgi0vbySTLBVAEAzyC05egOvpYLCyIGOtQYt+ouoIbNNY2NbPmWQcW+xzbH7+s1ROGLieKhtm+mp6Z5FwAMgaxaZMV8nQbYBv73iELzZdwJNiE3qEFmFynzkShWZVZiczIrVAoPFMiSTGHKTPbJhPc7SKf5nzDna4vSS1S1Oskio7iovPZ9b+tux+VVaUq2cezwfmLUOhidtBbsJENRPtD6GACAkpgyUlShqyviKZ9gt5EsMjm6751/dzx7/fw7bVOxBCUNVQyYUfv4CmOY00zWmkt72PZ377LNKWGGWomlLFX/7Te7BiNt07e/ifv/8fssnsaC2v/3975x5lVXXn+c8+r/usN1RZBWjxUFEQ8RGIKLGxi4CCDRVTIWo0DT5WWjNOZq2xhbjGadFZPnolK+jYycqoM5PYTZQoaCMo0jGQgYYhahTBB+OytKQKSupJVd3XOWfPH+feW3Xr3nrghaIs9metoureu+85v30OZ3/33r+9fz/A6+0fb/FGCamdvfv/bT87f7MjU3wAzdDQdY1l915PoMAPSCLyC9pC/w1XRJKlbIKJeZRG/g5IhaeW2A6Yhkw6tD1fB8lprd5pJ6+x9WIReQ7lRMLFdQfqo3u81dWQIQ7pug1UZ+D/dbdQF76c3x//c68PBAgIizaZPSUkEAQtg6KwP9l7lxQ4lZS2BjmayB5lBTWTm865DC0CuiYoLjgrS0qmhyv4oOsIiT4rlvyawa3Vl1EQ8mXaPAbFAZRAKBQZJByXWNxbb2/bvb1hXSO5mVaknaqFyQY/2h3DjtuEioMIUn4KmFf3TS69bjbNnzbjLwgwblIZxSUhOtp7+MP/+MOQ4gBgWAZnzzwbNIHjuiRsm//zz3/KEgcATddY8bMf4g/7ae2MIXGJT3oIRHtG3otu499JuFVYXUvSvfHURjzT1BAIXNGB7XsfpIUVn4WGL+lgdmnrjtPdE0sv5Uyt69eT0yqpWS0pwXYckNDXDz4c2t1ulgRnMcs3gU8Tx9CEYLI5jt2RT3i16z2mFR3m4rIGBPBe60QOtU/kXM6itTOKoQtMQ8MyDO4/59s88tkbHLO7cKS3RHhaYBxrz72WqoJCWhJeJNSUM15PLjM1dI3HZy3hoQ/fYF9bA6bQsaXL9yZezA/Ovmxw48cQSiAUCiSRuEtndyxDFPqioaHpYOrg4iaDunli4A/5oE+PMrUkFcAyghTMPgfX9RpITYDruDQcaBi6xUxOSU2cM43j3Z7PoqOpLadjOlkNIl0RzOTua4IHQYtmJ0XS4sQLXkPEzgVho8WmIrC8nroLPaGXiBRsAql7RuBiNN8F3bO8rxsGkQEc9CkSjhdWBAHTmcBe6gfNvNefWT4vh4YpdM6zerO3fdNfTVnF/6Kq4DCW7h1vWuGX9ERbqez6LrrQvClBCQnHJiB9rJ2whAa7jU4nynmh8VQEC/FZOkJIwkHL8+uklhH3uVg+Avzs4r+hJd5DS6ybiYEigoY17DqMBZRAKM5opJR0dMfpjiSGPU2QEgtD95ZeeiucZFoEpJQ4dNNlvklMP4TpVlKQWIhFGZZpYBhDzPUL0HWdcy6fwje+dwVmwMAN/gUZ3oPhk7hO7nl115UEwgEM3VtZ5JiDBHHT24iVP05KAHxtKwnG5xO33iUSfgVEwvtJYlesg/hZ4BQTjy8BBo627IoenPAepN6J7JlKRfd0LtHO5h33c+xkkHQTnSICHCM7l0G5VsAkqzTdaBuaAM1LzGOY71FdeBS0XrGxdAdf4DDS/TNG3MtS2Xe/iK4JzvVVYCRjKLmuJBqz6Yk5dHbGME0Nn6ljGt6ehP474cusIGVWcOBrOYZRAqE4o2nritMTGbw3PBiat3EAXSc9pR+lkcPWfUjiSBEDadJp/StFHX9PvH02HT0JJsyYxOH3szfImQGLH/7T7ei6lnTIusTHPYkbeB+0GL4CKJ91AUffDSP7CIWma0y4cCKhot6GTItPhYF67QIQvU7uWMmzmK1VREJbQcuVq8AFXyPQSLf/EwQ1GK11WaueXP+HuJW/wEB6AiMtZGwCS7+4l4sTk9hvf4ErXWaYE6jWx7Mz/jE74h9i46IjuWrcUf76rD306K+AG0Tv+hbm8UWYhh/T0Ij5d+e0T2oxYv7dlIj56Fpqya2Wuccj4wupKTAX23GJJFdlaZq3/yXgM9KiMVo3sY0ESiAUZyxOsid5sjlq/hKXrt7oriKBBDoK1hHqeRpdE/zVqgX8/oEXsGMJ7LidDtVRc9ci9GRuYwE4gXfT4pDiqgcOsf0/XUBXUwikBggKywtZ8KOF6fl/15XIeDmi5xJk8C+g9S7H9Tba9TNaxDnu/z1StuYO0Na3vBbDLXydnmNXo9llvZvvRAL3rCcyG3ARQ/gaEONeZkrrCqb4yjIOW2OcT03wfGKl/4JWuAOhxfuc6zhO8Sbc4Ds4TfeTSOjYIdJhtvtjaBp+MzMv9Ak5PiC9ECGR8K6Xrntxuvw+A8vQkxvczhyUQCjOWPSkMzMWP3lZuVxi9IiDGaG/U0gRxzXrMbSJlFWW8Le/+CEH/niAxg8bKTyriIv+ehZFZxUmcxN7xMJvZvWYAyU2S//nflr2zSV66GqKK0s467xKHAeicZtEIrn/ABBf3IZWtgVR8gfQIoBAaDlGTAIIvYeMjUO6OkIb4ppIDcfaT7R7DnrwM6RjIsx2AsjstltLIAv/hGxdkXZs9wYZFOD7HL1oR4aIZXzXasBXfAAreinx2FV0Bf8Mot8owvWhdV9JD7Y3VaRr2LQjcTEo+cp7EhxH0uPY9ETtPqMLk4BPxzLG5tLWvuQtEJFIhDVr1nDgwAF0Xee+++5jwYIFWeX27t3LnXfeSXV1NQCWZbFhw4b050899VQ6/3VtbS133313vqYpFIMjobjAR2tHlIQ9cEyer3TgYXzmC/m5dMllXLqk36oY4a31jxT8M47/3ZxHEQKqLtIIT7oIgM5InIS3+y25NFVLjgQ0aFnm/QCcexeQe0pNCNCsdkAgXYHQBquHhhb4jPCEF0itUZJSgwFiG0kRJxJzEBoYmo7PFBiGjqkLYgXvYItBRnJajIT1F6zopZjxWVixy4j73vJEQgCuDzM2C637Eo4Txza/oLvon3CMLxAITDmeKvs/EpDnD1KfoekdXcTo6hH4LJ1wwMTXf9QyhshbIJ555hnC4TBvvPEG9fX13HzzzWzbto1QKJRVdurUqbz00ktZ7+/bt4/XXnuNzZs3A1BXV8ecOXP4xje+ka95CsWgmLrG+JIAbcdj6XnofNDw4ZfnEuXjrFGEQMdypxIjd67ivsT9u4kG/y3nSAQA14cVuTJ1YExdJ6ElY10HP4TQu+D6ofMKSPSuAvJWJg2M0Gyka0DXpcjw+4ALwkb0t0PYmGX/njEaEeTeDyAlIBxMfyPEJ4IricUksZiL0AVaYIhuuNQRbih5DkGo/W581n5igV2AxIpegRm7GIGGK7o4XvoPSNGTFFqIi0Y+M/8rk+Pr8FEx2JmGjetKIlGbaMzGMHUKAt6oYizsnu5L3vkgtm7dyooVKwCorq5m5syZ7Nw5cHrGXGzZsoXly5fj9/vx+/0sX76cLVu25GuaQjEsNCEoK/QzriSA35d/zJxK+y40AgiZTB4jNYT0cVbiP+C3LMQwYvtHw5sHcBYDroEZm4UZm508PgR8OoVhDf3sdYiJT0DpNhj3Kkx+AIq3936361KkHOL8QsKRlfDxL+HQExCtRrreMl7pGuBaED07Y5VTny9niYR3PV2ofDartHQkTvulSDlYX1XHF5nf5wwCMz6LcMffEe64Cyt2CSLZlMWCO5DYWT4Kic1R+UrOXdj5ICUk4g6tHVGOtUeTO93HDnmPIBobG5kwYUL6dWVlJUeO5A6QVV9fT21tLYZhcNNNN1FbWwtAU1MTc+bMyTjGvn0Dx6cZiMFyq+bD+PEFp+S4I81YqMdI1CESS9DVkyASs/lqz/uFlLnP0pR4hePuQQLaRCrN5QTDXoiNgqBJJOoQS9heg5LjHB36AEtUJYTdb1Em70YUZfbvOo0dSPMjzzEMgAPCgYoN+MUcNHs8MrKCSMF7IHogly8CEG4hgVBxsjfsQ7auxfW9i+M7CG4hRs+VxMr+kVw6I4RMOs77x7IC/F8QKIoj3P73cCrx7hrs0HYQ8T676gRgUBr/WwrDU3Nfj37ErIbcvgxhY5uf4tga40oC6RhVJaXZMx35YEtBYYGfkN8cuvBJ4lQ+E0MKRG1tLY2NjTk/271797BPNGPGDHbs2EFBQQENDQ2sXLmSiooK5s2bN3xrh6ClpSsrbWS+fN0StA/EWKjHSNZBCPBpEIk5RGKJdGjq4eOnkO9RmHwVA2J0U1Iaovu4NzIw8ZpA23WJxW3iydhPSNDF+Tj+PdlTTNKHaJ/P8UT26KKj7HVvWW0WEvz/F73rOpxEMdbhR7BD23EL/wBGR8Y5pGvBkTp6jvdrZI9fSGrvg1Xgw+2eDOYXCJEpBNIxQcis9z0rbHq6IuBYSUeJtzzYZxgEOm+C2OXEgn/E1drQ3EL0xBR80bngltJJJOt4uXBDVRA2s8VP6hCdQHtPBB0XgaCkNERba/ewjnsidByPUFEcOOnHzUW+z4SmiUE71kMKRMpxPBBVVVUcPnyY0tJSwBsNzJ07N6tcONxrxKRJk6ipqeHtt99m3rx5VFZWZohQU1MTlZWVQ5mmUJwypPSmnkJ+g3DAwHElcdslGneIxmwcJ/eO6xPF0ASGpuO3dC9Eh+MF5DPi36PZ9w7QZye0NDESkzES5+W2WQzk23AQWhxT0zA1gGJIfBfZ8l2iwa1EQ68gteMIuxx/xwqEfTluQCJdiST127smqVwUouM6KNqTuZpIagg3nFwtle3PEQh8RV9gxMd74cGFQO87n5eYjtkx/UQvYQa+yF8RCb9MliNeGgRj11EYNE+5n8BJ5sc+XWlCTyZ5+yAWL17M888/D3hTSPv372f+/PlZ5Zqbm9Obgtrb29m1axfTp09PH2PTpk1Eo1Gi0SibNm3i2muvzdc0heKkkBILv6lTHLI4qyxIeWmQkkI/fp+XyzrvWP/S23Rn6hoBU6csMJnJ9qME3dkIaaHJAsKx6yg9/lN0Xcu5D8CKfhPcHFMb0sSMXpJ1PiEh0H0tJc2/pPTIc5Qc+znBxFwClk7IMgj7TQoCFoUhH0UhH8VhPyUFfsYV+Sn1TaKg5b+gx6d4U0pSx4zNprj1YTQ3Ow8F4J0wtB+frnkZ105BggTNLaSw5X40u8Lzlbg+NKeU8shqykPVWMapX3EU9Bte7K4xQN4+iNtuu43Vq1ezcOFCNE1j7dq16dHCunXrKC8v58Ybb2Tbtm2sX78ewzBwHIfly5dTU1MDwNy5c/n2t7/NkiVLAFi+fHmGT0KhGFVIb/WTqWuEAwau9MJd27ZL1HaJx21cR+L2S1l6oufwU8059j/0vieAwlTOBe/4rkym7XRcjMQS4vJPuG577xSL68OKzsGwJw/71AnrIJHw73HML9DscgJdtVixy+jNJuc17KY9haKWh5HE8eTNa040Zzyu2ZSjTro3wjjhS2FjWx8hRQIzPh0h/QOWFZrAJ6cR6PgFutWCaUoCYiLCOPW9eU0IwkGTglBq8vDrj5C5kuF+TVE+iIEZC/X4utRBCIHjuNiui+1IYrbr5UpwXIqKg7S2nPx5b+/E4NBDm7aVTm03mvRTmFhEwJ6H63rB8xzXxXG9eFHelFGmkzzm20d38VOZjl7XR7DzJvyRhQAUFgXo7BjYJxD3vUNX8RPZq7CkSdGX/4julA+7SgnrfbpK1iFxPd+1cAh23kIgWuNlr9O8LICmrmMk4yildzsP0RScLB+EpgksU6MwZOEz9RHdPHfafRAKheLEkFJ6jYamYxkQ9CVFw3UpLgqiu2468VDCdrDt1GgjjxEHeM5tgoxzbmCcc4P3nsDzhqdI5nWQ0sv0JpPndaU3MmkI/u/sVUBajEjhekL2NSBNL7OdrmXEYUqbLcFKXII/UkM0uA1vqZMA4RLuvA2TinTMqgxfgOjT5079rXfQVvyztOM9dY5I4XOMC0wl1DdgYN/rNgINdEoUgn4Ty/Q2/KV8NGMJJRAKxQggpZeZzpcMAgeArzcmUqpn77jeVFXC9hLyuE6vcEjyFBBINp7Sy32QXEmUwqYNV+TujQohCBcdwy+nUFISpE1Ligspx7XElSLdOJeJ20nEl9CjvYPAJOzOwfAXIZKzQ6K/ImQbyTHtVXLtzJbEadP/lZA9cETZk0k674UusAwNn+XdQ0Pv3fMx1oQhhRIIheI0kmpYNNGbbwJTR4jebr+TDCXuJnv93konF8d2SbgSeZJEROBloctpJw6aG6TvkCGddTn5jybIaOsNqgi4VYNUPuuPDBJ8icy1GU9IEqJ5kJp8NVIhwoUGuu6FALeSWfqM5KiJPtd3rIpCX5RAKBSjkL6Nj9d7hfTcTFI7RJ+pdifttE4KhStxpDcyScUQctzkiCQ5NZTKXZHOmkeAkHsJXdrb3ga7tDEaPjkJ6ySFqRguQTmdDvlHpOiXe1saBN2ZJ3Ss1LUSwltxJoTAZ2qEgiam7omAnswXYeginXQo47RngiL0QwmEQvE1pW97pWsCfZCVM6LPdI6Unlj0CoTng5CuJOz+Z96P/z0xjiJxEBgYIsxU8VN0S0e6Mh3V1DNigP5/eqAxcKOasn+g1a5F8iq+5F9IyESvYEmBhsV4/gYjudzXy/2Q/J3Mqa0nU6GmBEFLioIuSJYRjBsXxhig0T8DtSAnSiAUijMA2W86p3cTV2brHKCMK/1P0+a8S5dTT1CvYpxxGULo6fLjxoUJ6H1GH7I3s7XsPUVmMqE+ear7S4pMfyx6E/wkp3tK5X/nUOxXfGn/CYlDqTGb8/x3EzbO9hr/ftmuh9uwn4mjga+CEgiFQpGBEIJSYzalxuz0e/0FJu2D6Ofo7nekvG0xKOVi46fpBl30PZccfISiyB8lEAqFYtQjBhQhxalkjGwIVygUCsXJRgmEQqFQKHKiBEKhUCgUOVECoVAoFIqcKIFQKBQKRU6UQCgUCoUiJ0ogFAqFQpGTvPdBRCIR1qxZw4EDB9B1nfvuu48FCxZklfvNb37Diy++mH7d0NBAXV0da9asYe/evdx5551UV1cDYFkWGzZsyNc0hUKhUORB3gLxzDPPEA6HeeONN6ivr+fmm29m27ZthEKhjHK33nort956KwCJRIJvfetbLF26NP351KlTeemll/I1R6FQKBQnibynmLZu3cqKFSsAqK6uZubMmezcuXPQ77z55puMHz+eiy66KN/TKxQKheIUkbdANDY2MmHChPTryspKjhw5Muh3XnzxRb7zne9kvFdfX09tbS11dXVs3LgxX7MUCoVCkSdDTjHV1tbS2NiY87Pdu3ef8Ambm5vZs2cPjzzySPq9GTNmsGPHDgoKCmhoaGDlypVUVFQwb968Ezr2YLlV82H8+IJTctyRZizUQ9VhdDAW6gBjox6nsg5DCsRQvfmqqioOHz5MaWkpAE1NTcydO3fA8ps2beLqq69OlwcIh3sb9kmTJlFTU8Pbb799wgLR0tKF657c6I75JgUfLYyFeqg6jA7GQh1gbNQj3zpomhi0Y533FNPixYt5/vnnAW+aaP/+/cyfP3/A8i+++CI33HBDxnvNzc3pcL7t7e3s2rWL6dOn52uaQqFQKPIg71VMt912G6tXr2bhwoVomsbatWvTI4J169ZRXl7OjTfeCMBbb71FT08PV111VcYxtm3bxvr16zEMA8dxWL58OTU1NfmaplAoFIo8EHIMpVZSU0wDMxbqoeowOhgLdYCxUY9RP8WkUCgUirGJEgiFQqFQ5EQJhEKhUChyogRCoVAoFDnJexXTaELTTk1i81N13JFmLNRD1WF0MBbqAGOjHvnUYajvjqlVTAqFQqE4eagpJoVCoVDkRAmEQqFQKHKiBEKhUCgUOVECoVAoFIqcKIFQKBQKRU6UQCgUCoUiJ0ogFAqFQpETJRAKhUKhyIkSCIVCoVDkRAlEP15++WWuv/56LrzwQp577rlBy77wwgssXLiQmpoa1q5di+u6I2Tl0EQiEX7yk5+wcOFCFi9ezJtvvpmz3N69e7n44otZtmwZy5Yto66uboQtzeTTTz9lxYoVLFq0iBUrVlBfX59VxnEcHnzwQWpqali4cCEbNmwYeUMHYTh1ePLJJ7niiivS1/3BBx8ceUMH4bHHHuOaa67h/PPP5+OPP85ZZrTfh+HUYbTfh7a2Nu644w4WLVrE9ddfz49//GNaW1uzyg33eT9hpCKDjz76SB46dEjee++98re//e2A5T7//HM5f/582dLSIh3HkatWrZIbN24cOUOH4Mknn5T333+/lFLKTz/9VM6bN092dXVllduzZ4+sra0dafMG5JZbbpGbNm2SUkq5adMmecstt2SV2bhxo1y1apV0HEe2tLTI+fPny4aGhpE2dUCGU4cnnnhCPvrooyNt2rDZt2+fbGxslAsWLJAfffRRzjKj/T4Mpw6j/T60tbXJPXv2pF8/+uijcs2aNVnlhvu8nyhqBNGP8847j2nTpqFpg1+a119/nZqaGkpLS9E0jbq6OrZs2TJCVg7N1q1bWbFiBQDV1dXMnDmTnTt3nmarBqelpYWDBw+ydOlSAJYuXcrBgwezekxbtmyhrq4OTdMoLS2lpqaG11577XSYnMVw6zDaufzyy6msrBy0zGi+DzC8Oox2iouLmTt3bvr17NmzaWxszCp3qp53JRBfkaamJqqqqtKvq6qqaGpqOo0WZdLY2MiECRPSrysrKzly5EjOsvX19dTW1lJXV8fGjRtHysQsmpqaqKioQNd1AHRdp7y8POu69r/2g9VtpBluHQBeffVVrr/+elatWsU777wz0qbmzWi+DyfC1+U+uK7L+vXrueaaa7I+O5Hn/UQYU+G+h0NtbW1OBQbYvXt3+sEe7QxVj+EyY8YMduzYQUFBAQ0NDaxcuZKKigrmzZt3skxV5OD73/8+P/rRjzBNk127dnHXXXexZcsWSkpKTrdpZxRfp/vw0EMPEQwG+cEPfjBi5zzjBOJk9ZArKyszGujGxsYRHc4OVY+qqioOHz5MaWkp4PX2+g5VU4TDvQnLJ02aRE1NDW+//fZpEYjKykqOHj2K4zjouo7jODQ3N2dd19S1nzVrFpDdkz2dDLcO48ePT/995ZVXUllZyaFDh5gzZ85Im/yVGc33Ybh8Xe7DY489xmeffcavfvWrnNPfw33eTxQ1xfQVWbRoEdu3b6e1tRXXddmwYQPXXnvt6TYrzeLFi3n++ecBbwpp//79zJ8/P6tcc3MzMpkSpL29nV27djF9+vQRtTVFWVkZF1xwAZs3bwZg8+bNXHDBBen/9CkWL17Mhg0bcF2X1tZWtm/fzqJFi06HyVkMtw5Hjx5N//3BBx9w+PBhJk+ePKK25stovg/D5etwH37+85/z/vvv89RTT2FZVs4yw33eTxSVMKgfmzdv5vHHH6ezsxPTNAkEAjz77LNMmzaNdevWUV5ezo033gjA7373O55++mnA63088MADo2aKqqenh9WrV/PBBx+gaRr33nsvNTU1ABn1eO6551i/fj2GYeA4DsuXL+f2228/bXZ/8sknrF69ms7OTgoLC3nssceYMmUKd9xxB/fccw8XXXQRjuOwdu1adu3aBcAdd9yRdtCNBoZTh/vuu48DBw6gaRqmaXLPPfdw9dVXn27T0zz88MNs27aNY8eOUVJSQnFxMa+++urX6j4Mpw6j/T4cOnSIpUuXUl1djd/vB2DixIk89dRTLFu2jF//+tdUVFQM+rzngxIIhUKhUORETTEpFAqFIidKIBQKhUKREyUQCoVCociJEgiFQqFQ5EQJhEKhUChyogRCoVAoFDlRAqFQKBSKnCiBUCgUCkVO/j+HQhE2IZbDRgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm16 = GaussianMixture(n_components=16, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm16, Xmoon, label=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the mixture of 16 Gaussians serves not to find separated clusters of data, but rather to model the overall *distribution* of the input data.\n",
    "This is a generative model of the distribution, meaning that the GMM gives us the recipe to generate new random data distributed similarly to our input.\n",
    "For example, here are 400 new points drawn from this 16-component GMM fit to our original data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f0cffef2ca0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xnew = gmm16.sample(400)[0]\n",
    "#Xnew = gmm16.sample(400, random_state=42)\n",
    "plt.scatter(Xnew[:, 0], Xnew[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GMM is convenient as a flexible means of modeling an arbitrary multi-dimensional distribution of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many components?\n",
    "\n",
    "The fact that GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.\n",
    "A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the *likelihood* of the data under the model, using cross-validation to avoid over-fitting.\n",
    "Another means of correcting for over-fitting is to adjust the model likelihoods using some analytic criterion such as the [Akaike information criterion (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) or the [Bayesian information criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion).\n",
    "Scikit-Learn's ``GMM`` estimator actually includes built-in methods that compute both of these, and so it is very easy to operate on this approach.\n",
    "\n",
    "Let's look at the AIC and BIC as a function as the number of GMM components for our moon dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Y15ccxGZ38NObUknv3/SnfJ1BevYtUPQm9D2GYMvdifa9+SoMeh2jBsWw68hFKqqtbqxQCOHJLl9W+dKHewj2N/Kb/8pwedCDhH2r6JOvQqu+hL3gaL3t44bEYrM72HJQ3qgVQjT0w8sqf3VnOrHh/m6pRYZxWkHfYwjoDNhyd6CP7V+3vWd0IInRgWzYl09mRg83ViiE6Az7jhexeucZokJ9iQv3Izbcn9gIf4L8DG2+UuZ0YQWvfraforIa7sjsS2Z6glOvtmmJhH0rKEZf9D0GY8vdgTb6jnpt44bG8u5XRzh5vpzEGM+eY1wI0bTSCjN/X3YQRVE4cqYUs+XKFXj+Pvra4P/uBSAuovZreLAPaiMBvulAPv/+8jB+Pnp+MXc4fRNCXPiTNE7CvpX0vTKw5e3CUXgCoobXbR81MJoP1xxj3b5zzIvp38w9CCE8laZpvP3FISw2B0/ffRUxYX6UlJvJL6riXFEl+UVV5F+sZO+xi/U+PW/Uq8SE+REbUftCEBfuT87JEtbuPkv/HiE8MCvVZVfbtETCvpX0icNA1WPN3QGpV8Lez8dAer9IthwsYM6EPhgNbVsqTAjhfuv35bPveBF3XNe3bkw9LMiHsCAfBvWqf7VdRbWV/O9eAM5drORcUSXHzlxia3ZB3T6TR/Zk9vhkdKrnvC0qYd9KitEPXcIgbCe2o2n31WsbNySWLdkF7DxygdGDYtxUoRCiPS6UVvOf1UcZ0DOE6zISWtw/wNdA34SQBkMzZoud88VVKErt+3mexnNedroAQ68MtIoiLPnH623vnxhKRLAPG2RyNCG6FIem8ebyHBTgnqkpjY6/t5bJqCMxJtAjgx4k7NtEnzgcFB0VhzbX264qCuOGxJJzsoTCUpkcTYiuYtX20xw+XcodmX2JCPZ1dzlOJWHfBopPALr4FCoPbWmwuMDYwbEoIL17IbqIsxcr+eTbEwzrE8HVg2PdXY7TSdi3kT75Kmwl53EUnaq3PSzIh0HJYWzcn4/DIZOjCeHJbHYH/8jKxseo47+mDHDr9e+uImHfRvqkNFBUbLk7GrRdMySOknIzB3KL3VCZEKK1sjblcfJ8OXdO6u8xl0Y6m4R9G6k+gfgmDsJ6YnuDoZxhfSMI8DWwasdpp6whKYTouKOnS8jadJLRg6LJGOD6OWrcRcK+HfwHjEa7dB5Hydl62/U6lamjEzmQW8y2nEI3VSeEaIrFaudP/9lFcICRH13fz93luJSEfTv49R8JKNhObG/Qdn1GD3rFBvHe10coq7K4vjghRJM+W3eC0wUV3H3jAPx8DO4ux6Uk7NtBHxCCLrZfo+P2qqpw940DqDbb+GDV0UaOFkK4w+FTJXy9/TQ3jkkitVe4u8txOQn7dtL3ugpHyVnsJecatCVEBjBtTBJbsgvYc+yiG6oTQnxftdnGP5fnEBnqy93TBrm7HLeQsG8nfa90gEZ79wBTRycSH+nPOysPU222ubI0IcQPfLD6KEVlNdw3dSA+Ju+cJUbCvp1U/1B00X2x5TYct4faN2vvnpJCaYWZj7853ug+QgjnuzxT5ZSRiS5Z2NtTSdh3gD45A0fRaRyXGl+pKjkuiOszevDN7rMckoXJhXC58ioLb31xiITIAGZe3cvd5bhVq8LebDazcOFCbrjhBqZPn85vfvMbAHJzc5kzZw6TJk1izpw55OXl1R3TXFt3oe+VAVA77XETbrommcgQH97+8hBmq73J/YQQnUvTNN756giV1Vbum5aCQe/dfdtW/fQvvvgiJpOJlStXsmzZMh599FEAFi5cyNy5c1m5ciVz585lwYIFdcc019ZdqAHhqJHJ2E40HfYmg467pqRQWFLNkg25LqxOCO+2NaeAHYcKmTWul8fOROlKLYZ9ZWUlixcv5tFHH62bPyIiIoKioiKys7OZNm0aANOmTSM7O5vi4uJm27obQ3IGjot5OMouNLlPSmIo1wyNY+W2U+Tml7mwOiG8U0m5mXdXHqF3XBCTR/Z0dzkeocWwP336NCEhIfz1r3/l5ptvZt68eezYsYP8/Hyio6PR6WpXZtLpdERFRZGfn99sW3dzeSinqatyLrttQm+C/Y28tSIHm93hitKE8EqapvHWF7V/Z/dNG+hRq0W5U4vXINntdk6fPs3AgQN58skn2bt3Lw888AB//vOfnV5ceHiA0x+jvSIjv/tvYWQgZ2KS4fQuIjNva/aYn906jOfe2sa6/eeZc71z16utq89DSX0dI/U17YvNeRw4UcwDNw0mtX90o/t44/PXYtjHxsai1+vrhmSGDh1KaGgoPj4+FBQUYLfb0el02O12CgsLiY2NRdO0JtvaoqiowiOnC46MDOTChfIrG3qkYd7+CQW5eagBTX8yLzk6gBEpUXzw9WH6JwQTH+Hvmvo8jNTXMVJf0/KLKvnnkgMMTAolo19Eo3V05+dPVZUmO8kt/v8mLCyMkSNHsnHjRqD2KpuioiKSkpJISUkhKysLgKysLFJSUggLCyM8PLzJtu7I0MqhHIC5mf3wMep5e0WOR76QCdEVVZttfPrtcZ5+azt6ncI9N3ZsicHuSNFaMRfv6dOneeqppygtLUWv1/PYY48xfvx4jh8/zvz58ykrKyMoKIhFixaRnJwM0Gxba3WZnj1Q+clvUIy++M14qsXjNx88z9+XZXPHdX25/qoeLqnPk0h9HSP1XWF3OFi/L5/F605QVmVl1KBoZl/Tm/BgH4+orz2c1bNv1eeGe/TowTvvvNNge+/evfn4448bPaa5tu5In5yBZcdiHJUlqP6hze47amA0W7ML+HTdcYb1jSAypHuvfSmEMxzILeLDNcc4e6GSPgnBPHJLX5LjgtxdlseSt6k7ib7XVYCGLW9ni/sqisKdk/qjKgr/+vKQLHQiRBucvVjJnz7ay0sf7sVitfPQrFR++aM0CfoWeOeMQE6gC41DDY3DdmIHxkGZLe4fFuTDrRP68M7Kw2zYl8+4oXEuqFKIrqus0sLiDbms23MOk1HHbRP6cF16gtd/Mra1JOw7kb7XVVh2L8VRdQnVr+UJl8YPi2NrdgEfrDlGanI4oYEmF1QpRNditdn5escZsjblYbE6mJAWz4yxSQT6ecfasZ1FXhI7kT45AzQNW96uVu2vKgp3TRmAze7g3a8Oy3COEN+jaRpbswt46o2tfPLNcQb0DOXZ+0bwo+v7SdC3g/TsO5EamoASHIP1yHoMKdfWTS/RnJgwP2Zd3YuPvznOzsMXvGoBZCGacuzsJT5cfZTj58roGRXAPTcOIyWpe1667SoS9p1IURSMgydh3vAv7GcPok9IbdVxN4zowbZDhbz71WEGJIYS4Otda2MKcVlhSRWfrTvBtpxCggOM3H3jAMamxqKqcs18R8kwTicz9B+H4h+GeefiVg/L6FSVu6cMoLLGxgerZd1a4X3yiyr5R1Y2T72xlT1HLzJjbBLP/2QU44bESdB3EunZdzJFp8c4fHqbe/c9owOZMiqRrE15jBwYzeBk71sQWXifsxcqyNp8km05BRh0KpkZCUwe2ZOQALlYobNJ2DuBof84LLuXYd65GF38oFaN3QNMH5PEzsOFfLTmGKm9wlp9nBBdzenCCpZtzGXn4QsYDTomj+jJpBE9CfKXN16dRcLeCdrbuzfoVW4clcg/l+eQfbKEQfKGlOhmTp4vZ+nGXHYfvYiPUcfUMYlcn9FDrq5xAQl7J6nr3e/4vE29+xEp0Xy89hirtp+WsBfdxolzZSzbmMve40X4mfTMvLoXmRkJ+PvIxQiuImHvJPV692cOoO8xuFXHGfQq1w6PZ9nGPApKqogO9XNypUI4z7Ezl1i6MZcDucX4++i56ZpkrktLwM9HosfV5Bl3onpj9wmpre7dTxgez/LNJ1m94wxzr+/n5CqF6HyHT5WwdGMeOSdLCPQzcMu1vZkwPB5fk0SOu8gz70Tt7d0HB5gYkRLFhv353HRNsvyBiC5B0zQO5hWz8qO9HDxRRJC/kTkT+3DtsHhMRp27y/N6kiJO1t7efWZGDzYfLGDDvnynzHkvRGexOxxsP1TIl1tOcaqwgrAgH+7I7Mv4oXEYDRLynkLC3sna27vvFRtEn/hgVu88w3XpCfLBEuFxzFY7G/bls3LbKS5eqiEmzI+7pwxg+rV9KC2pcnd54gck7F3A0H8clj1Z7ejdJ/C3JQfZd7yIYX0jnFylEK1TUW1lzc4zrNp5hopqK73jg7jjur4M7RuBqigY9NKb90QS9i5Q17tf/3abevdp/SIJDTTx9Y7TEvbC7S5equarbadZt+8cFquDob3DmTIqkb4JwfIBwC5Awt5FDP2ubvPYvV6nMjEtnk+/PcGZCxUkRDa+tqQQznS6sIIvtp5kW3YhilK7rOakkT3lfOxiJOxdpL29+/HDaq+5X7XjDHdNGeDkKoWopWkah0+VsmLrSQ6cKMZk0JGZkcANV/UgLKjpxbyF55Kwd6H29O4DfA2MGhTD5oPnueXa3jL9sXAqh0Nj99ELrNhyitz8MgL9DNx0TTIT0+Ll065dnIS9C7W3d5+ZkcC6vef4ds9Zpo5Ocm6RwitV1VhZvy+fNbvOcKG0hqgQX+ZN6s/Y1Bi5fLKbkLB3sfb07hMiA0hJDGXNrrNMGtETvU6WIRCd4+zFSlbvPMOmA/lYrA76JgRzy7V9SO8XKZf7djMS9i5Wv3e/H32PIa067vqMHvzl033sOnKBESnRTq5SdGcOh8be4xdZvfMM2Xkl6HUqowZGc116Aokxge4uTziJhL0b1O/dD25V735In3CiQnxZteOMhL1ol8oaK+v31g7VXLxUQ2igidnjkxk3NI4gmWK425Owd4P29O5VReG69AT+s/ooufll9IoNckGlojs4e6Gidqjm4HksVgf9EoK5bUIfhveLQKfKkKC3kLB3k/b07q8eEsvn60+wasdp7p8+yAVViq7K4dDYe+wiq3aeIedkCQa9ysiB0WSmJ9AzWoZqvJGEvZu0p3fva9Jz9eBY1u4+y60T+sg6naKBqhob6/aeqxuqCQuqHaq5ZmicrAbl5VoV9hMnTsRoNGIy1YbL448/zrhx49izZw8LFizAbDYTHx/Piy++SHh47ULZzbWJWu3p3V+XkcDqnWf4ZvdZZo1LdkGVoqvYffQC/155mEsVFvr3CJGhGlFPq8+Cv/zlLyxZsoQlS5Ywbtw4HA4HTzzxBAsWLGDlypVkZGTwhz/8AaDZNnHF5d69o/AE9jP7W3VMdKgfQ3qH883us1htDidXKLqC8ioLbyw9yCuf7ifQ18iv78zgyR+lkTEgSoJe1Gn3mXDgwAFMJhMZGRkA3H777Xz55Zctton6DP2uRgkIx7xzMZqmteqYzKt6UFZlZVtOgZOrE55M0zS2Hyrk1//YyvZDhcy6uhcL7sogOU7evBcNtXrM/vHHH0fTNNLT0/nf//1f8vPziYuLq2sPCwvD4XBQWlrabFtISEin/gBdXXvG7gcmhhIf4c/XO04zJjVGZhz0QpcqzLz71RF2HrlAUkwgT9yeQkKUTEwmmtaqsH/vvfeIjY3FYrHwu9/9jmeeeYbrr7/e2bURHu65J29kZOdd0aCFTeb0vuU49i4jYviYVoX3rGv78Oone7lQYWVQcsP3QjqzPmeQ+tpH0zTW7jzN3xfvp8Zi566pA5k1vjc6D/tUtac+f5d5Y32tCvvY2FgAjEYjc+fO5cEHH+TOO+/k3LlzdfsUFxejqiohISHExsY22dYWRUUVOBytG9pwpcjIQC5cKO/U+9QNmYp5/duc372pVb371MQQ/H30fLzqMFE31Z9jxxn1dSapr32Ky2r498rD7DteRJ/4YO6+cQCx4f4UF1e6u7R6PPX5u6w716eqSpOd5Ba7A1VVVZSX1z6wpmmsWLGClJQUUlNTqampYceOHQB88MEHTJ48GaDZNtG4to7dmww6rhkWx64jF7h4qdoFFQp30TSNdXvP8Zt/buXQyRLun5nK/B+lERvu7+7SRBfSYs++qKiIhx9+GLvdjsPhoHfv3ixcuBBVVXnhhRdYuHBhvcsrgWbbROPaM3Z/XVoCK7eeZs2us9w2oY8LqhSudqG0mre/OETOyRIG9AzhrikDGNQv2qN7psIztRj2PXr0YPHixY22paWlsWzZsja3icZdvu7esmdFq8I+LMiHtP6RrNtzjplje2EyylS03YVD01i76yyffHMcRYE7J/XnmmFxqPJmvGgnz3pXx8spOj2GAeOx5x/CUX6xVcdcn5FAldnGpoPnnVydcJWC4ipeeG8X7319hL4JwTx770iuHR4vQS86RMLewxj6jAbAemxzq/bvEx9MYkwgq3acbvV1+sIzVdZYWbz+BAve3MaZC5XcOzWF/7ltKOHBsgyg6DiZG8fDqEGR6GL6YTu6CeOwaS1ehqkoCtdnJPCPrBwO5hWT2kumpOhqKqqtfLX9FKt3nqHabCejfyR3ZPYjNFDmPhKdR8LeA+n7jsG8/m0cF0+ii0xqcf+rBkTz0drjrNpxRsK+CymrtLBy2ynW7DqLxWonvX8k08YkyayUwikk7D2QIfkqzBvfxXp0U6vC3qBXmTA8niUbcjlfXOXxHxjxdiXlZr7ceopv95zFancwMiWaqWOSiI+QSymF80jYeyDF5I++51Bsx7egjZqDorZ8lc21w+NZvjmP1TvOMLi/rGTliYrLalix5STr9ubjcGiMHlQb8jFhfu4uTXgBCXsPpe83BlveTuxnDqLv2fJlmMH+RkakRLPhQD73V1tdUKForQul1SzffJKN+/MBGDs4hhtHJxEV4uvmyoQ3kbD3UPoeQ8Hkj/XYplaFPdQuSr7pwHm+3naKsQOjnFyhaElBcRVZm/PYfKAAVYVrhsVx48hEubpGuIWEvYdSdHoMySOwHtmIZqlGMbbcC0yMCWRAzxA+/Pow/eMCiZCeo1ucu1hJ1uY8tmYXoNepTEyPZ8rIRLm6RriVhL0HM/QdgzVnLba8nRj6Xd2qY+6aMoBn/7WD1xYf4Jc/Tsegl49SuEJFtZXdRy6w/XAhB08UYzTomDSiJ5NG9CTYX5YDFO4nYe/B1Og+KIGRWI9ubnXYR4X68dgdafzurW18sPoo8yb1d3KV3qusysLuIxfYcaiQnJOlODSNiGAfpo1JIjMjQdZ8FR5Fwt6DKYqCoe8YLLuW4qgsQfUPbdVxo1JjmTyyJ19uPUWfhGBGD4pxcqXe41KlhV2HC9lx+AKHTpWgaRAV6suUUT3J6B9Fz+gAWUxGeCQJew9n6Dsay64l2I5twTh0SquPmz0+mRPnyvjXl4foGR0o13B3QEm5mV3f9eCPnC5FA2LC/Jg6OomM/pH0iJKAF55Pwt7DqcExqFHJWI9ualPY61SVB2YO4um3tvPa5/v5zX9l4GOUX3drFZfVsPPwBXYcLuTYmUtoQHyEP9PHJpExIIr4CH8JeNGlyF9/F2DoOwbzxnexF51GF96j1ceFBJj47xmD+MMHu3n7i0P894xBElDNKCk3sz2ngD3Hizh0sgSAhMgAZo7rRUb/KOLkf0eiC5Ow7wL0vUdi3vSf2ukTwue06diUxFBuviaZT789Qd+EEK5LT3BSlV1TWZWFnYcK2ZpTyNHvhmiS44K5+ZpkMgZEyadbRbchYd8FqD6B6HoMxnZsM9qIW1HUtl1OOWVUIsfOXOKD1UfpFRtEclyQkyrtGqpqrOw8coFtOYXk5JXg0DRiw/2YOa4XI1KiGdxfVoIS3Y+EfRdh6DeGmlN7sJ/LQZ8wqE3HqorCvdMG8szb2/l/i/ez8O4RBPganFSpZ6qx2Nhz7CLbsgs5kFuEza4RGeLDlFE9GZkSTXykjMGL7k3CvovQ9xwGBt/a6RPaGPYAAb4GHpyVyvPv7uSNZQd57Nah3X7lI4vVzv4TRWzNKWTfsYtYbA5CA01MTEtg5MBokmICJeCF15Cw7yIUvRFD8lVYT2xDu/pOFH3bP3rfKzaIuZn9+PfKwyzflMf0sb2cUKl72ewOsvOK2ZpdyO6jF6ix2An0MzB2SCwjU6LpkxDc7V/khGiMhH0Xou87GuvhddjydtUtX9hW44fFcfRMKYvX55IcH8ygpLBOrtI9bHYHG/bls3xzHkVlZvxMejIGRDEyJZoBiSHo2vg+hxDdjYR9F6KL7Y8SEF47fUI7w15RFO6cNIBTBRW8vuQgT999FWFBXXcWRqvNwYb9tSFfXGamd1wQd2T2Y0jvcPQ6CXghLpO/hi5EUVQMfUZjP3MAR9Wldt+PyajjoZtSsdod/G3JQWx2RydW6RpWm4O1u84w//XNvLPyMKGBJv53zlCempdOWr9ICXohfkD+IroYfd/RoDmwHd/aofuJDffn7ikDOHb2Ep98c7yTqnM+q83Bmssh/9URwoN8+PmcYTz143RSe4XLG65CNEGGcboYXWg8akRi7fQJg2/o0H2NSInm6JlLfLX9NH3ig8kY4LkLnlhtdtbtzWfFlpOUlJvpkxDMPVNTGJgYKgEvRCtI2HdBhr5jMG/+D/aSc+hC4zp0X3Mm9iE3v4w3V+TQIyqAaA/7xOjlkF++OY/SCgt9E4K5d2oKKRLyQrSJDON0QfreI0FRsB3d1PH70qk8ODMVvU7l1c8PYLbaO6HCjrNY7Xy94zRP/m0z7319hKgQX564fRjzf5TGwKQwCXoh2kh69l2Q6heCLiEV67HNGK+6GUXp2Gt2eLAP908fyMsf7eXdrw5zz40pzYappmnUWOzUWOxUmW1Um23UmG1UmW3UWOzY7A50qoJOVdHplO++v3I7vKSG8vLqBu3qd1/3Hi9ixZaTXKqw0K9HCPdPH8SAniES8EJ0gIR9F2XoM5qatW9gzz+CPm5Ah+9vcHI408cmsXRjHpoGRr1aF971A91OjcWGpnXCD9GM/j1C+O/pgxiQ2LoFW4QQzWtT2P/1r3/llVdeYdmyZfTr1489e/awYMECzGYz8fHxvPjii4SHhwM02yY6Tp+UDnoTtmObOiXsAWaM7cW5oiq25RTiZ9Lha9LjY9LjZ9ITGOKL33e3fU16fL9r9zU2vK3XKdgdGjaHhsOhYbc7sDu0un+BgT4UFVde2WbXsDtq93E4NKJCfembENIpP5MQolarw/7gwYPs2bOH+Ph4ABwOB0888QTPP/88GRkZvPbaa/zhD3/g+eefb7ZNdA7FYELfKwPrie2YxvwYRd/x9U5VVeGhWamdUF3zIiMDuRDU9ukehBDt16rBXovFwjPPPMPTTz9dt+3AgQOYTCYyMjIAuP322/nyyy9bbBOdx9B3NFiqsZ3a6+5ShBAerlU9+z//+c/MmDGDhIQrC1/k5+cTF3flsr+wsDAcDgelpaXNtoWEhLS6uPDwgFbv62qRkYHuLgEtfASn1oWintxG5MiJ9do8ob7mSH0dI/V1jDfW12LY7969mwMHDvD44493+oO3pKioAofDye8EtkNkZKDHLG6hJo+kav/XFJw+h+pTe4J4Un2Nkfo6RurrmO5cn6oqTXaSWxzG2b59O8ePH+e6665j4sSJnD9/nnvvvZeTJ09y7ty5uv2Ki4tRVZWQkBBiY2ObbBOdy9B3DGh2bMe3ubsUIYQHazHsf/KTn7BhwwbWrFnDmjVriImJ4Z///Cf33XcfNTU17NixA4APPviAyZMnA5Camtpkm+hcuvCeqGEJWDvhA1ZCiO6r3dfZq6rKCy+8wMKFC+tdXtlSm+h8+j5jsGz7CMel86jBMe4uRwjhgdoc9mvWrKn7Pi0tjWXLljW6X3NtonMZ+ozCsu1jrEc3Y8q4yd3lCCE8kMyN0w2oAWHo4lOwHtuM5uyPtgohuiQJ+27C0Gc0WlkhjsKuMze9EMJ1JOy7CX2vDNAZ5Y1aIUSjJOy7CcXoiz5pONbjW9HsVneXI4TwMBL23Yih7xgwV1J1bLe7SxFCeBgJ+25El5CK4hNI+d7V7i5FCOFhJOy7EUXVYUjNpOroDmz5h91djhDCg0jYdzPGIZPRBYZj3vwfNM3h7nKEEB5Cwr6bUfQmwib8CMfFvE5Zo1YI0T1I2HdDAanjUCN7Yd72CZrV7O5yhBAeQMK+G1IUFZ/Rc9GqSrHsXeHucoQQHkDCvpvSxfRFnzwCy94vcFQUubscIYSbSdh3Y6aRtwEOzNs+cXcpQgg3k7DvxtTACIyDJ2M7thl74Ql3lyOEcCMJ+27OOGwqim8QNZvflxkxhfBiEvbdnGL0xXjVbBwFx7CdkKULhfBWEvZewNBvHGp4T8xbP0KzWdxdjhDCDSTsvYCiqphG34FWUYRl/0p3lyOEcAMJey+hj0tBn5SGZc9yHFWl7i5HCOFiEvZexDRyDtitWLZ/5u5ShBAuJmHvRdTgaAyDMrEeXo/94kl3lyOEcCEJey9jSpuBYvL/blZMuRRTCG8hYe9lFJM/xoybsOcfwnZyl7vLEUK4iIS9FzKkXIsaGod5y0dodpu7yxFCuICEvRdSVB2mUbejlRVgPbjK3eUIIVxAwt5L6XsMQddjMOZdS3DUlLu7HCGEk0nYezHTqNvBasayY7G7SxFCOJmEvRfThcZjSJmANWct9pKz7i5HCOFErQr7hx56iBkzZjBr1izmzp1LTk4OALm5ucyZM4dJkyYxZ84c8vLy6o5prk14DmPGLDCYMG/5wN2lCCGcqFVhv2jRIpYuXcrixYu55557eOqppwBYuHAhc+fOZeXKlcydO5cFCxbUHdNcm/Acqk8gprSZ2E/vx3Z6n7vLEcKtrIfWUfXFH7FfzHN3KZ2uVWEfGBhY931FRQWKolBUVER2djbTpk0DYNq0aWRnZ1NcXNxsm/A8hkGZKEHRmLd8gOawu7scIdzCkr2GmnVvYj+TTdXnv6Vm03tolmp3l9Vp9K3d8Ve/+hUbN25E0zT+8Y9/kJ+fT3R0NDqdDgCdTkdUVBT5+flomtZkW1hYWKuLCw8PaOOP4zqRkYEt7+RGba2v8oa7KPhkEabTWwjOmOykqq7obs+fq0l9HfPD+sp2fUX5hn/j1yedyGk/pWT9R5TtXIkjbyfhN9yD/4BRKIritvo6Q6vD/ne/+x0Aixcv5oUXXuDRRx/t9GJ+qKioAofD8z7SHxkZyIULnnu5Ynvq00IHoItLofib/2COGYZi8ndSdd3z+XMlqa9jflifJXst5g3/QtdzKOr4ByiuUiH9dvx6jKBm/dsUfvYHdD2G4DN2HmpQpMvrawtVVZrsJLf5apxZs2axdetWYmJiKCgowG6v/W+/3W6nsLCQ2NhYYmNjm2wTnklRlNoPWpkrqfn2TRyl591dkhBOZ8n5pi7ofa//GYrOUNemi0rG76aFmEbfgf38ESo//hXm3VlO/9S5s+asajHsKysryc/Pr7u9Zs0agoODCQ8PJyUlhaysLACysrJISUkhLCys2TbhuXQRiRjTZmA7uYfKj+ZTlbUI6/GtMqWC6JYsOd9gXv82uh5DGgT9ZYqqwzh4Ev63/h/6nkOwbP+Eqs8WYMs/3Gl1aJqG/eJJzNs/pfLjpzjz+qNOCXxFa+FeL168yEMPPUR1dTWqqhIcHMyTTz7JoEGDOH78OPPnz6esrIygoCAWLVpEcnIyQLNtrSXDOO3T0focVaVYD6/HeuhbtPKLKD6BGPqPwzBgPGpwtNvrczapr2O6Qn1n1y27EvQ3PNxo0DfGdmoPNRvfRSu/iL7fOEyjbkP1afv4uuZwYC88hi13J7bcHWgVRaAo6GIHED5yCtWRQ9p8n9D8ME6LYe9OEvbt01n1aZoD+5mDWHO+wXZyN2gOdPEDMaRciz4xDUXX6rd8nFKfs0h9HePp9ZlOb+biF6+3Oegv02xmLDuXYNm3EsXoi2nUHPT9rm7xDVzNbqudbTZ3B7a8XWjVZaDq0SUMwpCUji5xGKpvkNPG7Nv31yq8gqKo6HsMRt9jMI7Kkrrefs2q11B8gzD0u7p2Bs2gKHeXKkSrWHK+obyFoZuWKHoTppG3oe87BvP6f1Hz7T/RHV6P6er/QhcWX29fzWbGdvoAtryd2E7uAUsV6E3oew5Bn5SOvudQFKNvJ/10LdQtPfu28/SeizPr0xwO7GcOYM1Zi+3UHtA0dPGDanv7ScNR1Jb7D978/HUGqa99Lo/R+/Yejm78gyh6Y4fvU9McWA+vx7z1I7DUYBw6BUNqJvaz2bVDNKf3g90CJn/0icMx9EpHFz+o2ceWnr3wCIqq1vZKeg6p7e0fWvddb//V2t5+/2tqe/uBEe4uVYg6lkPf1o3RR9/yC4pKzJ1yv4qiYhwwHn3icMxbP8KyJwvLntoLUxS/EAz9r0bfKwNdbL9WdYScScJetJvqH4opfSbG4dOxn96HJecbLHuXY9m7An2f0RiHTUUXGufuMoWXsxz6FvO6t+qGblS9EeicsL9M9Q3C99r7sPUfh/3cIfQJg1CjklEUz5lrUsJedJiiqugTh6FPHIajogjLvpVYD32D7egm9ElpGIdPRxeZ5O4yhRe6EvSDa8foO2Hopjn62P7oY/s79THaS8JedCo1IByfMXMxDp+G9cDXWA6uwpa3E11Cam3ox/Rzd4nCS9QP+oedHvSeTsJeOIXqG4TpqtkYh96IJXsN1v0rqV72PLrovlRdeytaUF+XzjUivIv10DrM696WoP8eCXvhVIrRF9OwqRhTr8d6eB2WvV9w/sP/Qw3vgXHYdPS9MlBUzxnXFF2f9dA6ata9hS5hkAT990jYC5dQ9EaMgzIxpFyLb8EeitZ9Qs3q11CCozENnYq+75h2f0hLeBfN4UCrKUOrLEWrLMFRVYJWWYJWVYqjsgT7mYO1QX/DIxL03yN/XcKlFFVP4JAJVEenYcvbiWV3FjXr3kTZubj2GuUB16DoTS3ej6Zp4LCDzYxms3zvqwVUPUpAGIpPoFcOFWma1qV+bs3hALsVzW4BmxXNUo32XYA7qkrrBblWVYpWdQk0R/07URQU32AU/1AMAydgGnW7BP0PSNgLt1BUFUPyVeh7ZWA/sx/L7izMm97DsmspuoTU2j/+78L7yldz/VD/4R/8D+kMKAFhqP5htV8DwlH8w1ADwlACwmu3u+jTi86gaVptCF7Iw36x9p/j4km0qlLQ6UE1oOgNoKv9p+j03329vE1f972iN4BqAL0BRdWBpn03GZcGlz93We+2Bho/uF37tdCop6ay8srv0G5Fs1trg9xurf3dfW8bWgsL5pj8Uf1CUfxDUEMTUP1DUPxDUfxCUP2++943qLZu0SQJe+FWiqKg7zEEfY8h2M4fwbJnOfbzR2p793ojit6IYvJD8Q/97vaV7fVuG65s12xWtMpiHBVFaBXFOCqLcZzNwVZVciW4LjP61Ya//3cvBgFhlMclYNcCUIIia3uLHtBL1jQNrbIY+8U8ig/mU3XqCI6LebXzqwAoCmpILLr4gbUfaLPbamcrvRyq3/2r22YzQ00FmsOKZrPW38/hAAVAAUX53lfq3Vaa2O7Q6XCoehSdse6FRDH6ofgaQG+88oKjN3739fILkLH2e4NPbZB/F+jSQ+8cEvbCY+hj+qGf7LxLMzWHvbYnXFGMVlFU97X2haEYW+EJNHMFF75/kM6AGhiBEhiJGhiBGhiJEhiBGhRZ+70TFnnRNA2t4iL2C7U99boee03tR+hrFBU1NA5dj8HoIpLQRSShhvesfcHzAJ46XYK3k7AXXkNRdbXDNwHhQN9G99FsZkIMNRSdzMNRfgFH+UW0stqv1oJjtRNZfZ/RFzUw8sqLQGAkio//dz3r7w1d2K0NhzPs9XvUl3vYjspiMFd+V7QONSwOXc9h6CIT0UUkEdV/IEWlFuc+WaLbkbAX4nsUvQljRAR6LbjRds1ciaP8Io7yC2jlF3CU1X7vKM3HcXnSq6bUjZ1/f+jiyni6YvJD0RnQRfVCvdxjD0toMIyhGkyAhL1oGwl7IdpAMfmjM/mji0hs0KZpGlr1JbBUXwnxy2+QqnqPGPsX3kvCXohOoigKil8I+IW4uxQhGpCPLgohhBeQsBdCCC8gYS+EEF5Awl4IIbyAhL0QQngBCXshhPACHn3ppap67nXJnlwbSH0dJfV1jNTXMe2tr7njFE374cxQQgghuhsZxhFCCC8gYS+EEF5Awl4IIbyAhL0QQngBCXshhPACEvZCCOEFJOyFEMILSNgLIYQXkLAXQggv4NHTJbhLSUkJv/jFLzh16hRGo5HExESeeeYZwsLC6u03f/58Nm3aRGhoKACTJ0/mwQcfdEmNEydOxGg0YjKZAHj88ccZN25cvX2qq6v55S9/ycGDB9HpdDz55JNMmDDB6bWdOXOGn/70p3W3y8vLqaioYNu2bfX2e+WVV3j//feJiooCIC0tjYULFzqlpkWLFrFy5UrOnj3LsmXL6NevHwC5ubnMnz+f0tJSQkJCWLRoEUlJSQ2Ot9vtPPfcc6xfvx5FUfjJT37Crbfe6tT6WnsegvPPxaaev9ach+D8c7Gx+lp7HoLzz8Xmfpd79uxhwYIFmM1m4uPjefHFFwkPD29wHx1+DjXRQElJibZly5a627///e+1X/7ylw32e/LJJ7V33nnHlaXVmTBhgnb48OFm93nllVe0X/3qV5qmaVpubq42ZswYraKiwhXl1fPcc89pv/3tbxts/8tf/qL9/ve/d0kN27dv186dO9fgeZs3b562ePFiTdM0bfHixdq8efMaPf7zzz/X7rnnHs1ut2tFRUXauHHjtNOnTzu1vtaeh5rm/HOxqeevNeehpjn/XGyqvu9r6jzUNOefi039Lu12u5aZmalt375d0zRNe/XVV7X58+c3eh8dfQ5lGKcRISEhjBw5su72sGHDOHfunBsrap8vvviCOXPmAJCUlERqairr1q1zaQ0Wi4Vly5Yxe/Zslz7uD2VkZBAbG1tvW1FREdnZ2UybNg2AadOmkZ2dTXFxcYPjV6xYwa233oqqqoSFhZGZmcmXX37p1Po86TxsrL62cPa52FJ97j4Pm/pdHjhwAJPJREZGBgC33357k+dVR59DCfsWOBwO/vOf/zBx4sRG29966y2mT5/OQw89xPHjx11a2+OPP8706dN5+umnKSsra9B+7tw54uPj627HxsZy/vx5V5bImjVriI6OZtCgQY22L1++nOnTp3PPPfewe/dul9aWn59PdHQ0Op0OAJ1OR1RUFPn5+Y3uGxcXV3fb1c9lS+chuO9cbOk8BPefiy2dh+C6c/H7v8sfnldhYWE4HA5KS0sbHNfR51DCvgXPPvssfn5+/PjHP27Q9j//8z98/fXXLFu2jBtuuIH77rsPu93ukrree+89li5dyqeffoqmaTzzzDMuedy2+vTTT5vsTd1+++2sXr2aZcuWce+99/LQQw9RUlLi4gq7hubOQ3DfudgdzkNw7bnY0u/SWSTsm7Fo0SJOnjzJyy+/jKo2fKqio6Prts+aNYuqqiqX9VYu/5fVaDQyd+5cdu3a1WCfuLg4zp49W3c7Pz+fmJgYl9QHUFBQwPbt25k+fXqj7ZGRkRgMBgDGjh1LbGwsR48edVl9sbGxFBQU1IWi3W6nsLCw0eGA2NjYekMornwuWzoPwX3nYmvOQ3DvudjSeQiuOxd/+Lv84XlVXFyMqqqEhIQ0OLajz6GEfRNeeuklDhw4wKuvvorRaGx0n4KCgrrv169fj6qqREdHO722qqoqysvLAdA0jRUrVpCSktJgv8mTJ/Phhx8CkJeXx/79+xu9UsJZPv/8c8aPH193hcgPff/5y8nJ4ezZs/Tq1ctV5REeHk5KSgpZWVkAZGVlkZKS0ujVLpMnT+bjjz/G4XBQXFzMqlWrmDRpktNrbM15CO45F1t7HoJ7z8WWzkNwzbnY2O8yNTWVmpoaduzYAcAHH3zA5MmTGz2+o8+hLF7SiKNHjzJt2jSSkpLw8fEBICEhgVdffZWZM2fyxhtvEB0dzV133UVRURGKohAQEMAvfvELhg0b5vT6Tp8+zcMPP4zdbsfhcNC7d29+/etfExUVVa++qqoq5s+fT05ODqqq8sQTT5CZmen0+i6bNGkSv/rVr7jmmmvqtt1///088sgjDB48mCeffJKDBw+iqioGg4FHHnmE8ePHO6WW5557jq+++oqLFy8SGhpKSEgIy5cv5/jx48yfP5+ysjKCgoJYtGgRycnJDWq12+0888wzbNy4sa7t8ptlzqrv5ZdfbvI8BFx6LjZW39/+9rcmz8Mf1ufsc7Gp3y80fh6Ca8/F5jJl165dLFy4sN6llxEREUDnPocS9kII4QVkGEcIIbyAhL0QQngBCXshhPACEvZCCOEFJOyFEMILSNgLIYQXkLAXoovZunVrg2vGhWiJhL0QQngBCXvhESZOnMg///lPpk+fTnp6Oo899hhms7nZY1atWsXMmTNJS0sjMzOzbrrXgoICHnjgAUaMGMH111/PRx99VHfMK6+8wiOPPMLjjz/O8OHDmT59Orm5ubz++uuMHj2a8ePHs2HDhrr9582bxx//+EduueUW0tLSePDBB+vNSLh69WqmTp1KRkYG8+bNqzfbZEs/09q1a5k5cyYZGRncfvvtHDp0qMVjq6qquP/++yksLGT48OEMHz6cgoIC9u3bx80330xaWhpjxozh+eefb/fvQnRT7ZiHX4hON2HCBG327Nna+fPntZKSEm3y5Mna+++/3+T+e/fu1dLS0rQNGzZodrtdO3/+vHbs2DFN0zRt7ty52sKFC7WamhotOztbGzlypLZp0yZN02oXqUhNTdXWrVunWa1W7YknntAmTJigvfbaa5rFYtE+/PBDbcKECXWP8+Mf/1i7+uqrtcOHD2uVlZXaz372M+3nP/+5pmmaduLECW3o0KHahg0bNIvFor3xxhtaZmamZjabW/yZDh48qI0aNUrbs2ePZrPZtM8++0ybMGFCq47dsmWLNm7cuHrPx2233aZ9/vnnmqZpWkVFhbZ79+4O/kZEdyM9e+Ex5s2bR3R0NCEhIUyYMIGcnJwm9/3kk0+YPXs2Y8eOrZv0q3fv3uTn57Nr1y4ef/xxTCYTKSkp3HrrrSxZsqTu2IyMDMaNG4der2fy5MmUlJTwk5/8BIPBwI033sjZs2frzcs+c+ZM+vXrh5+fH48++ihffvkldrudFStWMH78eMaOHYvBYODee++lpqam3lzoTf1MH374IXPmzGHo0KHodDpuuukmDAYDe/bsadfzodfrOXXqFMXFxfj7+7tkjibRtUjYC48RGRlZ972vry9VVVVN7pufn0/Pnj0bbC8sLCQ4OJiAgIC6bXFxcfVmNfz++p4+Pj6EhobWLWByeZKq7z/296c8jouLw2q1UlJSQmFhYb2FJy5PWfv9x2rqZzp37hxvvfUWGRkZdf/Onz9PYWFhu56P3/3ud+Tl5TFlyhRmz57N2rVrm9xXeCdZcFx0SbGxsZw6darB9qioKC5dukRFRUVd4F9ekaq9vr9yVX5+PgaDgdDQUKKiojhy5Ehdm6ZprX6s2NhYHnjggXYtCq4oSoNtSUlJvPTSSzgcDr766iseeeQRtm7dip+fX5vvX3RP0rMXXdItt9zCZ599xubNm3E4HBQUFHD8+HFiY2MZPnw4L730EmazmUOHDvHJJ58wY8aMdj/W0qVLOXbsGNXV1fz5z39m0qRJ6HQ6pkyZwrfffsvmzZuxWq28+eabGI1Ghg8f3uJ93nrrrXzwwQfs3bsXTdOoqqrim2++oaKiosVjw8PDKS0trZtLHmDJkiV1C18EBQUBNLnQifBO0rMXXdKQIUN4/vnn+b//+z/OnDlDREQECxYsoHfv3rz00kssXLiQcePGERQUxMMPP8yYMWPa/VgzZ85k/vz5nDhxghEjRvD0008DkJyczIsvvsizzz5LQUEBKSkp/O1vf2t2kZHLBg8ezLPPPsszzzzDyZMn8fHxIS0trW7h6eb07t2bqVOnkpmZid1uZ/ny5axfv57f//731NTUEBcXx5/+9Ke6ISkhQOazF6JZ8+bNY8aMGdx6663uLkWIDpH/5wkhhBeQYRzhsf72t7/x+uuvN9ienp7OP/7xDzdUJETXJcM4QgjhBWQYRwghvICEvRBCeAEJeyGE8AIS9kII4QUk7IUQwgtI2AshhBf4/6J2ExU8/imZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(1, 21)\n",
    "models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(Xmoon)\n",
    "          for n in n_components]\n",
    "\n",
    "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n",
    "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('n_components');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimal number of clusters is the value that minimizes the AIC or BIC, depending on which approximation we wish to use. The AIC tells us that our choice of 16 components above was probably too many: around 8-12 components would have been a better choice.\n",
    "As is typical with this sort of problem, the BIC recommends a simpler model.\n",
    "\n",
    "Notice the important point: this choice of number of components measures how well GMM works *as a density estimator*, not how well it works *as a clustering algorithm*.\n",
    "I'd encourage you to think of GMM primarily as a density estimator, and use it for clustering only when warranted within simple datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: GMM for Generating New Data\n",
    "\n",
    "We just saw a simple example of using GMM as a generative model of data in order to create new samples from the distribution defined by the input data.\n",
    "Here we will run with this idea and generate *new handwritten digits* from the standard digits corpus that we have used before.\n",
    "\n",
    "To start with, let's load the digits data using Scikit-Learn's data tools:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next let's plot the first 100 of these to recall exactly what we're looking at:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, ax = plt.subplots(10, 10, figsize=(8, 8),\n",
    "                           subplot_kw=dict(xticks=[], yticks=[]))\n",
    "    fig.subplots_adjust(hspace=0.05, wspace=0.05)\n",
    "    for i, axi in enumerate(ax.flat):\n",
    "        im = axi.imshow(data[i].reshape(8, 8), cmap='binary')\n",
    "        im.set_clim(0, 16)\n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have nearly 1,800 digits in 64 dimensions, and we can build a GMM on top of these to generate more.\n",
    "GMMs can have difficulty converging in such a high dimensional space, so we will start with an invertible dimensionality reduction algorithm on the data.\n",
    "Here we will use a straightforward PCA, asking it to preserve 99% of the variance in the projected data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 41)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(0.99, whiten=True)\n",
    "data = pca.fit_transform(digits.data)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is 41 dimensions, a reduction of nearly 1/3 with almost no information loss.\n",
    "Given this projected data, let's use the AIC to get a gauge for the number of GMM components we should use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(50, 210, 10)\n",
    "models = [GaussianMixture(n, covariance_type='full', random_state=0)\n",
    "          for n in n_components]\n",
    "aics = [model.fit(data).aic(data) for model in models]\n",
    "plt.plot(n_components, aics);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears that around 110 components minimizes the AIC; we will use this model.\n",
    "Let's quickly fit this to the data and confirm that it has converged:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "gmm = GaussianMixture(110, covariance_type='full', random_state=0)\n",
    "gmm.fit(data)\n",
    "print(gmm.converged_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can draw samples of 100 new points within this 41-dimensional projected space, using the GMM as a generative model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 41)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new = gmm.sample(100)[0]\n",
    "data_new.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can use the inverse transform of the PCA object to construct the new digits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NlkIIIUQETZZCCCFEhNRu2MmTJzstFKQ+ffp0p02bNs1pe+65p9OOOOII7JPil2JQpZNQhYI99tjDaVQtgFxcIWdbrFoAQa7hSy+9NHU/G0NRYqHQ4iwVOyg8mlyvZmatWrVyGsX27bTTTk4LhdhnqeBO52MoJu+qq65y2oknnug0chWG4u7SOgvJDRuqZkGRZlsCuv5CFXqoghGFflPEJr1PVuiY3nnnndiWKozQ90TRjQMHDsQ+KeIvxvLly51G91YzdmzTvbV169apx5EGuuY7deqEbT/88EOnnXbaaU474IADnEbXqZncsEIIIURe0WQphBBCRNBkKYQQQkTQZCmEEEJESG3woRi2YsV4zi1btqzTKAJv0qRJTps3bx722bBhw9gQHbvvvrvTKObMzKx69epO69Kli9PoOIRi2LIYfNq2bes0MruExjJixAinHXPMMU4LmZKyGHw6dOiQSDMzu/baa532yiuvOO2QQw5xWuh8ywKZMyi2z4wNEFTLkExTFJ9mlt7gs2DBAqd9++232Pb77793Ghk7zjvvPKddd911qcZVGGSMqVSpEralc3n8+PFOmzp1qtNCUZVZoikpDpPqKZqZ/fvf/3YamZKIPn36pBtYIdC9K1QXmCLlyIyXps8sBjs6TqH7HNWxfeedd5zWt29fp11wwQXYZ8WKFSMj/P/ol6UQQggRQZOlEEIIEUGTpRBCCBFBk6UQQggRIbXBh5IzyKBjxgvBTZo0cRot6IaSJ7JQq1Ytp/Xs2RPb/vrrr4n6XL9+vdNKliyZbmCFQHUmQ3XeqGYdpXmQKaJFixYZRpecjz76CHWqwTl27FinjRs3zmnNmjXDPnfZZZd0gzOzGjVqJNLMzBYvXuw0MihQKkgaI0FayLRjxsYYSoEaOXKk00LHMokhJbd+LBmQQqlfZLgi4wglv4SujyTkjpnSqOg9zZIbW8gItDljTkLI9ESJUlSvlQw+WYw8IeieGTIdkknunHPOcdodd9zhtJD5Mg36ZSmEEEJE0GQphBBCRNBkKYQQQkTQZCmEEEJESG3woZSHNm3aYFsqaUQlVcqXL++0UIpDFtKk0Xz66aeJ2oVKLuULKhMVOiYrV650WrVq1ZxGaRchgw+lnoRKV22ATE81a9bEtmRKokX4ZcuWOY2MSmZm7dq12+Tf+TQimJn9+OOPTiNDGBmEYscuRK5JrnTp0q4NfddmZrNmzXJa06ZNnTZs2DCnkdnDjE0uuYlKucf9+uuvd68hs5SZN9qYmV1++eVOozSqqlWrYp9JyB3zqaee6tqEkriefvppp3333XdOo9SqkJmFiCWB0fVHKU5mfB598sknTiOzWj4TfMhIRqlYZmaPP/6408hgR+axChUqpB5bLvplKYQQQkTQZCmEEEJE0GQphBBCRNBkKYQQQkTQZCmEEEJEyGbRy2HXXXdFfdttt3XaihUrnNagQQOnkUM2n4QcsuRkpBqa5cqVc1rx4sU3f2CFEIrTO/vss51GdQHJ4UifIyvkkgs5eKmeIbl6L7nkEqdR5OLfAdWpJP71r3/l7T1zHYY777yza0POYjOz2267zWl0rtSuXdtpoTjIJLVEc9scdthhrk2pUqXwtXR/oBq4zZs3dxo5PJOSO+Z9993Xtdlvv/3wtXTPeOSRR5wWuk8SSc+1jaHvJtchvgFy8997771O++2331KPIw10zwzFWdL5fP/99zuNIhP33ntv7DP3nlWYo1e/LIUQQogImiyFEEKICJoshRBCiAh5WbMMraVVqVLFabRWEUum+DuhpBVaX6O1o38SO+64o9NozGnSjfIJfeeUwBIqP7UloDFTeg6lnhQloXUWGkflypWdRsc4n+dFmmQXWnejYxxa89wS0FppUZZkS0Poe6T7A92vi9qHQYTSrug+/PPPPzutqK6/gr9C2UVCCCGEMDM9hhVCCCGiaLIUQgghIuRlzXLevHmo9+3b12n0jPnYY4912plnnol90v6jLGueoaohtB+HnlTvtddeThs8eDD2Sfs0Y2sBVH0h9JoRI0Y47aWXXnIa7U2jfYz55KOPPkKdqs9QtQCqOBGqSrBxpZSCgoJE61pUSaRPnz7YlqoyrFmzJtHraX+jWfq1QTpvaa+ZmdmCBQucNn36dKdR5Yfx48enGldh0Pd68sknY1s6X2gv8OTJk50W+r7p+o2to1IFnFGjRmHbW265xWm0/k5jTvP+JUqUSPz6GM8//7zTPvjgA6fR9RfyqGSBrp8777wT277xxhtOoz2uI0eOTPz+afZZ5mWyDG2g/eGHH5y2fPlyp9EEWtSElmoXLlyYqG3ZsmWdlqbcTj6h47do0SKn0ab/ooYuejOzb775xml04dDkQDdfs/B3Whj0RwlNoGY85tWrVzutKM9nKpEV+l6pfBGVjqJjkE/oe6F7gxlff3SMi9pqQf2Hvlcac5Lwhi0JHVO6N2+J4xw6n+me9ncaAP/Z36gQQgjxD0CTpRBCCBEh9WNYegS2zz77YNuuXbs6jTJLX3nlFaeF1udy134KCgqia5ZUlX3o0KHYlh4LNG7c2Gm0J+nLL7/EPkOZkoVBmYyhteH77rvPaYcccojTvvrqK6fRo0+zbOsSy5YtcxpVhzfjx6u0v4oebc+ePRv7bNGixX//O+nePhofrTeZmQ0cONBplKf59ttvO+2MM87APnPzQmPjHjdunNNC2bDHHHOM0w444ACn0bpUPpkyZYrTPvzwQ2xLx5g0OsYdO3bEPtPs89zAsGHDnBZaS0s65iVLljgtlIGd5THuqlWrnFanTh1se/zxxzvtzTffdBqdW61bt8Y+aYkg9jnIb3HzzTdj26OOOsppr7/+utPofNvYz5AV/bIUQgghImiyFEIIISJoshRCCCEiaLIUQgghIqQ2+NBenD322APbUnA3bdy/5pprnEYbqs2yBRDQZl4qJGrGxhha0CajUvXq1bHPUDBwYdDCeP/+/bEtFaqlfaC1atVyWj6DkqnQ86uvvoptqeD3oYce6jQyf51//vnYJxUbj0EmmI2NQhtDxiIyhJHhLVQEO635pFu3bk4j046ZWf369Z1GYQAXXnhhqjGkhfbCUSi2mdmAAQOc9vjjjztt6tSpTuvUqVOG0TGvvfaa01q2bIltacxk8KF7J12nZtnuGTfddJPTQmEYV155pdPIgESmwpDBJ4spiY5z6D532WWXOY0KRc+aNctpZNI0S3f/0y9LIYQQIoImSyGEECKCJkshhBAigiZLIYQQIoImSyGEECJCastV5cqVnUZxa2Zm+++/v9NGjx7tNHJGjh07FvtMW9LIjF1eIebOnes0ipGiMlFZYu1CUERfqKwYVcMgF1uvXr2ctn79euwzSzkgqnIRgqIBP/vsM6dRebOQGy+Ls7dp06ZOo3PAzGzMmDFOo+oZFBWY5bwlqAxVbmTeBqh013bbbee0LC7iNNB18dRTT2HbL774wmlUQoxK5OUTKi9IEZRm4RjKXOjema/zwsysWrVqTnv44YexLblhX375ZadRrGc+OeGEE5y2ww47YFu6J06aNMlp5JrN4i7ORb8shRBCiAiaLIUQQogImiyFEEKICJoshRBCiAibv+pp4SghMmyMHDnSaVQzLRQPloWXXnopcdvVq1c7rV69ek478cQTnUbRZ1kJmUwIMv40b97caRR/lk/mz5/vNDKkmPFxJig2LEt9whBk3ipTpgy2PeWUU5xGBo3hw4c7jWL1zMxatWoVG+ImUM3AkEmETFRktrn++uud1qhRI+wzS6QcGa9CZrjJkyc7bfr06U6jmDM6NmbZYtjat2/vtJBR8NJLL3UaxRKWLl3aaevWrcM+sxh/TjvttERaCDJNLVq0yGlff/01vj4U91kYJ510ktN+/fVXbHvQQQc5ja5JMu1RHWYzNryF0C9LIYQQIoImSyGEECKCJkshhBAigiZLIYQQIkLBXyldKWvWrHHatGnTsC2ZO6iOHdWQpEV9s3C6Q2FQzbS2bdsmfv0TTzzhNFpsrlq1Kr6eDnHMpDJz5kynhcwVK1eudNqECROcFjJi5Qsyy5BRwszs3XffdRottpNpqGLFithnrsEjibGDTCHLli3DtpQkQwYNMn+FkpJyk2zyaV6i+olkHKFkIjruZmZDhw7d/IFZOI2K6i+SoeSBBx5wWu3atTd7XIURqs3arl07p1HN1WHDhuV7SHmFEnwoISc0ZQwZMiQv43j++edR7969u9PICEmJVCEjT5r0Kv2yFEIIISJoshRCCCEiaLIUQgghImiyFEIIISKkTvCh8kMrVqzAti+88ILTzjrrLKfRYj+9T1aoVFgoIYMMG1OmTHHagQce6LSQiYNMG7FyUpQa1KNHD2xLposXX3zRaUVt8KHvLJTqMWPGDKeRQeiPP/5wWiip5c8//9zk30kMPmRYGzBgALY944wznEalf9KUhMsHoXSScuXKOY1KilGCFh33rND94ZprrsG2ZKY76qijnHbRRRc57fjjj8c+W7Roscm/ixUrhmatjaFrmY6nmVmdOnWcRsk3ZPoJnWu551VBQQEmAGWFUodofGTQC6U75ZYA3GqrrYKmxw3QeRYqz0j3LzJv0jWde2/YwMb31IKCgmDimJl+WQohhBBRNFkKIYQQETRZCiGEEBE0WQohhBARNFkKIYQQEVLH3RHffvst6rvttlui11OMVJs2bbAtOSGz1KsLjbljx46J2oYcwPmCvhZyMpqZnXPOOU6rXLmy06jOYsj1uM0228SGmAiqT2jGNeeINKdnroORnKq5UCQcuafNzBYsWOA0itFq2LCh0+68807sc5999okNcRPI6de/f39se+uttybqc/fdd3cauanN2PkZg9y6FBdpZvbpp58m6pNciyGHee55X6pUqWB90Q3QdXHddddh26uvvtpp5Jyl+1TNmjWxzyuvvHKTf2+33XbWsmVLbJsFipS76qqrnPbJJ58k7vPxxx/f5N8lS5a0zp07F/oaOjcGDRqEbZ955hmn/f77706j67RGjRrY58bO22222cYaNGgQGqp+WQohhBAxNFkKIYQQETRZCiGEEBFSJ/gQobWCatWqJXp9mjIp+SI0Zioh9k8hNGZKIwmljfzdlChRAvWk50ZRQ+tItN5rxikgdO5SCbF8rQFTGlTZsmWxbdJjTJ83yXpvUmjMoeuMys0RlBYVuj5y1zezpoPtuOOOqNNxprZ0roXKzeWuhef7Hklr7TSWNN6M3OMaKou1MXRuhI4znTO0tkzXaeia3vi6DKW6bSAvBh8hhBDifzJ6DCuEEEJE0GQphBBCREi9MLF06VKn5abNb2Du3Ln+DWEthCpTjB49GvssU6ZMZISe3377zWlUtcDM7O2333Zat27dnHbeeec5LfSsvaihdYV77rnHafPmzXMaVYExM9xvFFvHonGEqiq8/PLLTqOKL0RozWncuHH//e+tt97aatWqlai/pFB1Djp+tIct6Z7jfPLkk0867f7773fasGHDnFa3bt2iGNJ/+fjjj1HP3V9oxlVHTjrpJKeF1pyogkiWNWTaD25m9s033zjt+++/T6RVqVIF++zdu/cm/y5WrFgmH8KECRNQpz24s2bNchrtT3z44Yexz1iFEYIqDYUq0tCaJe2Bv/baa50WWj/NXYUsbM9+6smSFk9Dm+XpJKITmkwg+VxKpb5o0jfjMdMkECoTtSWgsZBRgkpH0abefI7jp59+wrYLFy50WtLJMlRGJ+nrs0J/dNHFGirV9nfz66+/Oo1KRxX1cSNC593ixYudRiX8tgQUCGHG46OwC7r+Qn/45ev+EirfRseZrkn6oyKf5zfdm5ctW4Zt6VjR/aWobDh6DCuEEEJE0GQphBBCREj9GJaeu4dyVnfeeWen0Vpf69atnbbDDjukHVoQehz11FNPYVuqRj5q1Cinfffdd0677bbbsE/av0T7izaGHo2F1mRoLfKFF15wGh2HDz/8EPvcb7/9Ch0fQY92DjzwQGx79tlnJ3r9xIkTnUbrsWab7i0N7bnLZfXq1U4LHecLL7zQafSYa9q0aU4LZVPGzoMkhPYmnn766Yle/9VXXzktNF7a75dlTyY9DjYzmz59utPIp3D44Yc7LXTO5uux3O2334560rU+OldCOcS5xznJeULX8hFHHIFtu3bt6jTKy73iiiucNn/+fOwzdM4Uxueff+408jOYmVWoUMFptPZNucPnnnsu9nnCCSfEhvhf9MtSCCGEiKDJUgghhIigyVIIIYSIoMlSCCGEiJB6ZZ5Cu0ML/CeeeKLTLrjgAqfR4nU+ixKTcWTXXXfFtscff7zT9thjD6fdcsstTqOF/tB7xQwoZDKhoqZmvJGb9h/RfrD69etjn1kKalNfof5pYf/99993GpnHbrjhBuyzfPnysSE6aM8mHU8zHvNOO+3kNDJShQwaueaTLIafkEmErhW6rkImECJfezKPPvroxG3JgPTBBx84rXbt2vh6Mu3FIOMXGbfM2GRCm+DJoBIiiympXr16Ths/fjy2PfLII53WvXt3p1E4RWEFktNCxc/p3mrGpswWLVo4jb6n5s2bZxjdpuiXpRBCCBFBk6UQQggRQZOlEEIIEUGTpRBCCBFBk6UQQggRIS9VR/bcc09se/PNNzuNnKXkms3ieg1Bbt2Qc45KdM2cOdNpVBUgNOak0WsbQ8f5nHPOwbavv/56oj4pqixUVizLmImpU6eiftVVVzmtTp06TqtZs6bT9tprL+wzFFNXGG+99ZbT6Lw147JQY8eOdRq5YX/88UfsM+TKDkHlhyju0Iwdj88++6zTyCUditDLUmqMHLiha2XEiBFOe/zxx502ZswYpzVt2hT7DDmyC4Pctj///DO2bdmypdOo9Nbw4cOd1qhRI+wziyuajimVNzPjCioUkUkl6NKes4VBFafatm2LbSlukipe0T2cIkfTol+WQgghRARNlkIIIUQETZZCCCFEBE2WQgghRITUBp+NawZuIBQPVr16dacNGTLEaVRbLWTWyLLwTYYQGoeZ2UUXXeS0SZMmOa1jx45O23777VOPLQTV9QvVeWvXrp3TyLjz4osvOi1fRp4QPXr0QH3u3LlOW758udPI1NSwYcPNHtcG7r77bqdR3UEzNtKsX7/eaX379nUaxQ+amV199dWxIW4CRSqGYv7IzEOkqR2bJYYtjVmPvu/OnTs7jeosktnDLJvBh4yIoXsG3V8ee+wxp51yyilOIzOKmVnZsmUjI/SkuZZLliyZSMsSFZgGik+89dZbsS19v/vuu6/TyFy1atUq7DPN59MvSyGEECKCJkshhBAigiZLIYQQIoImSyGEECJCaoNPmTJlnNakSRNsS6kljzzyiNPItLD33ntjn1kMPsTBBx+MOtVUvOOOOxJp+ar1Z8Y1Cr/88ktsSyk0lCzz22+/OY3q7uUTSmQx4wSfd955x2kTJ050GqV+JCXXoEL1KEOpRkuWLHEamYHI8EbpPzSe2Pk9cuRIp5Fxy4zrfpIh6cknn3Qa1WgMvT5UzzYLZCCqVq2a06gG57Bhw7DPZs2aOS025sqVKzutd+/e2JaMfXQO3XPPPU6jeq1m2Qw+WWrQbky/fv2cRqk5F198Mb6eEsJikJEzlEhGtWdPP/10p9F5P3DgQOxTBh8hhBAij2iyFEIIISJoshRCCCEiaLIUQgghIqRemackhOeeew7b3nLLLU6jtAsqwxRarCYDQMwUsXr1aqctWLAA206ePNlpU6ZMcRqV66lbt26h49hcatWqhTqlw8yYMcNpZASiUmMhPWYgoNJUDRo0wLb0nbRv395pacw8uWOm8eaeKwMGDHBtyHxkZvbpp5867bjjjnNanz59nBYybOSWYoulsFCCVpcuXbAtneN0DtB3FPre8mVi+/zzz1GnFCcqmfb77787jcpqmZktXrx4k38XL17cKlWqVOj4qP8bb7wR29aoUcNpX3zxhdMogSaU+pXlPkf07NkTdXrfhQsXJuozVG6OjFgxyCBHx97M7JJLLnEalU+kcyuLYSoX/bIUQgghImiyFEIIISJoshRCCCEiaLIUQgghImiyFEIIISKkdsOuWbPGaaF6luR0Iucs1dML1c3L4hKj/z98+HBsSy42iqSi+LJQTFpuzFxBQUGmyLaQc5XceFTjkMYXcrhmic6iKLQ2bdpg2/nz5zvtlVdeSfQ+uQ7SDWQZ8y677JK4LUUDUlwWOe9C312W+pC5hI7Hrrvu6rTatWtv1nttbqTaBv744w/UBw0a5DRyIZOrPm1t0MKgGpyhY0c1cMltSnF3tBPAjI9PmrqgGwg5pc8//3ynkRP5zDPPdFromiGndKgu8QbonhGK4KR6vm3btnXaa6+95rQsUXy56JelEEIIEUGTpRBCCBFBk6UQQggRIfWaJSWMUDkbM05iyPLcfXOhNUsqzWRmVqFCBafRelNofTLp++cTWkeideCqVas6LZ/llWgcFStWxLa0vpGv9bCigtaZq1SpsgVGsimh84vWU0Pn/d9N6D5A66x03lK7ULml3HtWLCUpBJWIMuPxlSxZ0mn5WDdLS2j9j+7Z9PkoMSqf9zPqi+7BZry+T/fhorrfFvyVD4eBEEII8T+Yf/af8kIIIcQ/AE2WQgghRIS8LFi98cYbqFOFA3ou3rBhQ6d17Nhx8wf2/6BqGLQ3ysxszz33dBo9qZ40aZLTWrRogX3mJv8n2WdJ6739+/fHtrT+s2LFCqf98ssvTrvsssuwz3r16hU6PoKqKhx11FHYlvbg0ueg8+XRRx/FPkNr54VB+7y+/vprbHvHHXc4jdam6LMtW7YM+7ziiiv++99bbbUV7pmNce+996J+3333OW3vvfd2Gu1V23fffbFPOsaxde/cqh9mZhdccAG2DVUOyWXw4MFOC+3/O+ywwzb5d0FBQab1wzlz5qBOlWto3Yz2LDZt2hT7zLJ+T1VmQvck8jR07tzZaddee63TQntkiSweFdqDbWbWsmVLp9E5Tu1Cq41p1jfzMlnSzcGMN7nSgaagg3xCB2rp0qXYlgwp9Hq6AVDZrtDrsxC64dLES2W7Vq5c6bQ0J34M2hz/3XffYVv6zulz0Obu0Cb8fBEqQ0XHlMZH5cdC51s+Sl7RH0FmfOypNBWNl/6IyAp9X/SHlVnyMlFUKjBNuasshL4r+iw02YXuk/mCvrPQ8aTgDLpfbwlC5x59lqI+phujx7BCCCFEhLz8sjz++ONRJ0s1FQgdPXq000KFjqkobSxSif76mDVrFralX1o0lltvvdVpoaKlsfER9Mvr/fffx7ZUdDo3Ys/MP44yC9vhsxR/HjhwoNO+//57bBt6/JsL/bUbGnMW6FfP0KFDse0jjzziNFpCoF89FJlotumvoSRbGj788EOn3XTTTdiWHqvRI+z69es7LfR4MIstf+TIkU4LPTKnz0fnPR3j/fffH/sMbZ9Iy8knn4w6XWv0uHvevHlOo4LnZtmuvyFDhjgtdK3QPe3+++93Gt3nQktIoUjHtNByR4hOnTolapeP7ST6ZSmEEEJE0GQphBBCRNBkKYQQQkTQZCmEEEJESG3w+eqrr5xG+xjNzM4991ynnXXWWU6jhemQ5ZkWzmNQvmHIdHPppZc6LWm9yCxGnhB0TEMGkKQGjdatWzstn7UhyeDUuHFjbLvHHns4jcwOdJzzuXWETAnvvfcetqU9XbSPlPYtdu3aFftMuzeU9jSG9lnSVqbnn3/eaZRvG8pZzXJeUH7n9ddfn/j1/fr1cxqZl/bbb79U40pLyMD39ttvO61Zs2ZOCxmE8kUao9b06dOdNnXqVKeReSlk8MlXtvPMmTNRv+uuuzL3GdqOkiYbW78shRBCiAiaLIUQQogImiyFEEKICJoshRBCiAiaLIUQQogIqd2wFM4cqpQQckLmcuCBBzrt888/x7ZZqpxTin0o9JyiuSgq6aSTTnLawQcfjH1Swn+M119/3WmhiL7ddtvNaRRrRjFS7dq1Sz22EIceeqjT6HOYcdUJ0sgZl6W6SAhyXe+8887Ytk2bNk6j40znFlWmMEt/PtepU8dpoZD2c845x2nkDO/SpYvTKGg7K6eddlrithR3R8yePdtpIRcluURjkOP6gQcewLa77rqr06hCCV1r+XBpbuDCCy9MNA4z3qlAsaUUK5hPpzRVSpkxYwa2HTNmTOr+N5APp65+WQohhBARNFkKIYQQETRZCiGEEBE0WQohhBARUq8iU10+qqdoxtF0VLW8ZMmSTgtF6GWhYsWKTqM6bWZmFSpUcBqZDiiu65hjjsE+zzvvvNgQHfvss4/TJk+ejG3JWPPOO+847YknnnAamRNC7x/jgAMOcNqNN96IbWvXru00igMbPHiw09LUu4tB517IyEFxZzS+hx56yGnbbrtthtF5Nq5/uQGK1zMz69Gjh9PIkEQ1YkORfyEzX2FQjdgzzzwT277xxhtOo3vOunXrnPbll19in/ky+IQMixMmTHAa3UdeeuklpyWtx5iEZcuWOa1Ro0bYls5lik2k6yOf0Pf9008/YdtDDjnEaWSE6t27t9POPvvsDKPbFP2yFEIIISJoshRCCCEiaLIUQgghImiyFEIIISKkNvg0adLEaUOHDk38ekrDoXQTqr2YlTJlyjjt6KOPxraU9EAGmiVLljgtlKRCpiY6DhuTxWCzMVRbc8WKFU6jupJZITNByGBAXHfddU4bOHCg0/KZ1EJpQKG0DzpP6XuiRKpQDc60CT5kbAnVUb355pudRrVj6RhMnDgR+8xi8KF6ll988QW2pWuoV69eTjv11FOdRulGWaFzgGpAmvH5OHbsWKetXr3aaffffz/2SZ8v956RW4uVjG+hGpyvvPKK05Ka0KgGrFm2lJyQOZQgo9eRRx7ptHvuucdpNG+ZedNWYfdl/bIUQgghImiyFEIIISJoshRCCCEiaLIUQgghIqQ2+NSqVctpy5cvx7ZkiHjyySedttdeezmtZ8+eaYcWhBaGzz//fGxLaSifffaZ0yhlgkrkmMXNPASVeTrqqKOw7RVXXOG0Bx980GlkJslnQgeZT66++mpsS2k/zz33nNMo/YWMElmhY0LmLTMuEXTppZc6jQxl+WLt2rVOo+NmxmacESNGOG3NmjVOCyU70fexzTbbYNsNlCpVymlVqlTBttWrV3capSRRn/mErtkzzjgD25JBisa3++67Oy10feQm+xQrVsyVjss1DqYpBdi3b1+nNW3a1Gl0bnTs2BH7zL13FhQURL8nOiYhyEx3+OGHO43mGDJcmW1qMCooKMCErA3ol6UQQggRQZOlEEIIEUGTpRBCCBFBk6UQQggRQZOlEEIIESG1G5a47bbbUKe6Yscee6zThg8fno9hBCGXWKhmGsWBdenSxWn9+vVzWii6ieKhYtFQJUqUcFrIoXjiiSc6jaK/xo8fX+h7bkwW1+PKlSudRpFrZma//fab0+jzXXbZZU7bf//9Cx1HGtavX++0UBQbfWft2rVL9D4UeUjEnNPktJ0/fz62PeGEE5y27777Oo3Oi+bNm2Ofq1at2uTfxYoVi54Xixcvdtrzzz+PbWfMmOG0whyKGxOKdqNrKQa5pEPRdOPGjXMaOaffeustp9H3YeaP81ZbbeXcsLljbN++vesn5Pr/8ccfnUa1TumanjdvHvZZqVKlTf5dokSJ4OfbANX9/Pzzz7Et7ZqYMmWK044//ninUf1hs3Rxk/plKYQQQkTQZCmEEEJE0GQphBBCRMjLmmUoBYZSOsqVK5ePt0wFrQPRs3IzXl8sW7as02idJktSTwjqa5dddsG2VatWdRp9viwldNJA/e+2227YltaX6POVLl168weWktAaFyW1pC2xVRSEEoOqVavmNDovkpZmMvPfcZJzno4RnbOhtv8UQmuzVIKM1t/p+6hYsSL2udVWm96akxyX3NeE3tPM3PqnGfsUyO8RunfmXjextewQoZJzoc+SC322fFDwV1LngRBCCPG/FD2GFUIIISJoshRCCCEi5GXN8u2330Z94MCBTvv6668T9RnaF3PEEUds8u+CgoJo5YwffvjBab169cK2rVq1chpV06C1tHxWSlm6dKnTQhUK6Ek6rUMdeuihTuvQoQP2mWVvGu3J6tq1K7b9888/nUYVbej1tIfUzK8pJlnnoTXqV155BdueffbZTku6PtK9e3fUNz5nklRpoAo6tJ8y1JagdWXaq2ZmdvLJJ2/y7yTXHx1j2ptoZnbxxRc7jc4Luhbo/M4nc+fORZ32mb/55ptOGzVqlNOoasbfwaBBg5x23333OY3u4bnnwAaK2hNBe/SpIhR9H1RNKi15mSypbJCZ2ffff++0hQsXJurz119/RT3LEivdmGmjtBmXxqKF76Je6qUx0wQaGst2223nNCptlc/PQTfFRYsWYVv6fPQHCJ1bFCSQT6gskRmfu6FzPxf6Q8Is/fGnz07XmVnya43+qKDrwCx/50vo+qYx07lMoRZFDf3RbMbX5TfffOO0LTHmECtWrHAaHfvccIQtCf3ooeMcun43Fz2GFUIIISJoshRCCCEi5OUxbGgd8sADD3Ranz59nEYZsqG9Nln27lB25kcffYRtp02b5rTWrVs7rWHDhk4LPR6k/U8xXn/9dadRBXAz3vfUuHFjp3388cdOa9KkCfZJFcxje+roc86aNQvb1qtXz2n0qPLee+91Gq1rmYX3dBYGrbO8//772JaO85577uk0ygAN5dmm3UdKa32hJYVu3bo5jb5vWmagz2XGj0Rj0PhC5zLtzZ4zZ47T6Lwiv0FWKDuVrikzswYNGjjt3XffddpDDz3ktD322AP7rF69emSEHloGueqqq7DthAkTnEbfyS233OI0uh+ahbOxC4OWaUKeBLonHXnkkU47+uijnRZaLkm1xzhxSyGEEOJ/KZoshRBCiAiaLIUQQogImiyFEEKICHkx+Jx11lmJ9RdeeMFptMi60047YZ9ZgpZp43goDJiKz4YCzIsSMjBQkLeZ2Xfffee0pAWnQ/vdsoTCf/rpp4nbksGAwqdpHL/88gv2meXcoH1kZGowY3MNGcKmT5/utE6dOqUeG0GbsEOfm4oVxwIEigK6fg4++GBsW758eaeRMSYW3rC5kMEwVFy6Zs2aTqM9i6NHj3ZaKLSDzGqxTf90zYcKmdO1RkEkVFw5n/ucyeBG+8HNzCZOnOg0GjO9PrRfVAYfIYQQIo9oshRCCCEiaLIUQgghImiyFEIIISJoshRCCCEipHbDkhNx0qRJ2PbRRx91GkWubb/99k577LHHsM/OnTvHhugoW7as06jqhZnZzTff7LQhQ4Ykeh9yo5llK12z3377Oe3222/Htu+9957TQm7DXOjYZ2Xq1KmJ21566aVOa9GihdOqVq3qtObNm6cbWCGQG48iGc3MOnbs6LRbb73VaaeccorTKFLOLH1842GHHeY0couamQ0YMMBpN954Y6r3ywcUY1itWjVsW6ZMGafR5yO3fD6vvx122MFpofPigQcecNrs2bOddsUVVzgtdByyjJnuaeeeey62HTZsWCKNYg+zRI6GoOtvxIgR2JbKslHFF3IS56Pii35ZCiGEEBE0WQohhBARNFkKIYQQETRZCiGEEBFSG3zWrVvnNKo5aMZmoLlz5zqN4ujITJGVihUrOq179+7YdujQoU4j48ANN9zgtCyL8iGoNl8odq9Zs2ZOo6izE0880Wn0fZqF64kWBtX7o7qfZmbPPvus09asWeM0qm9Yo0YN7DNLDUDiq6++Qp0MSFS3kGohhupDnnnmmanG1qFDh0TjMmPDBhnHjjvuuFRjSAuZdlq2bIlt77rrrkR9kmkvn9ffihUrnBa6JmrXru20H374wWkUbReKsMwCxR5SLV8zjk388ssvnUb3dor3yyfnnHMO6hR9SfeCBQsW5H1MZvplKYQQQkTRZCmEEEJE0GQphBBCRNBkKYQQQkQo+Ouvv/5K8wKq6RbqYvjw4U4jAw0tNlNdOzNexM5SezHEM88847QuXbo4LeVhywuh1CFKBqGajMuWLXMaJWhkhcxCIVME1XwcP36807799lunUZKHWTgNpTDomFx77bXYlhKpKEGkfv36Ths1ahT2edBBB23y79i5TLX6QukkNA4yTFHNwiy1QdMQun5q1arlNEo/ohquRU3IWHbllVc67YMPPnAapQ4NHjwY+8zXPY3MjWac7rR48WKnUQ3Jt99+e7PHVRih9DYyZXbr1s1pZM569dVXN3tc+mUphBBCRNBkKYQQQkTQZCmEEEJE0GQphBBCREid4EML/19//TW2pdI1p59+utMqVaqU+P1zzQwFBQVWokSJQl9DZgAqoWPGyTIVKlRwGqW0hBJ2siSLrFq1ymnTpk3DtosWLXIaJQCRqeaQQw7BPrfaKvWpgQakUBrORRdd5DQqv1auXDmnkUklK2S6oLJbZmxYo8QZMh1Qik0Wli9f7jQqe2fGKTJJS7eFDDhZjCeUzPTiiy9iWzpfjj/+eKetXbvWadtuuy32mWXM1H/ISFWnTh2nffHFF06bMGGC08icZ2ZWqlSp2BAd9J2FSvCVLFnSaW+++abTQvf2ooTMUWZm/fv3d9qgQYOc9uCDDzotVMZu42s1Npfol6UQQggRQZOlEEIIEUGTpRBCCBFBk6UQQggRQZOlEEIIESG15ZFckpMmTcK25Lgi9xK5uEIOttzaklljofr164c6OTrJsUY1OEOuV6qHGXPI/vrrr04bMWIEtqW6oYcddpjTGjVq5LQsrtcQNI7DDz8c29L4evfunajPfEaxUUTfnXfeiW3pPKVakDvssMPmDyzA+vXrnXbsscdi2913391pN910k9PoeOYzznG77bZzGsVmhhgzZozTyBU8evRofH3IpV4YNOYnn3wS2x5xxBFOozqVnTp1chrFF5plc8PSvfC9997DtkceeaTTqPZl6JgWJbfddhvqdC+h72m33XZzWs+ePbHPja9/uWGFEEKIzUSTpRBCCBFBk6UQQggRIS8LVqGUiFB5mM0h97l8kjVLWpMJjY3WF/NZxiopNObQ2gs9t6d1s3yWMiNoHTaUtpN0HSlL+tHmEvq+qQRYUR/TXGiNOVSajJKx8rlGvTmE1uSSllnbddddnVbU50poPatq1apOo9SvHXfc0WlFPeZQ/zQ+KoUWSkXaEtCYaX2S1otDCVobX7+xazl1PUshhBDifxt6DCuEEEJE0GQphBBCRMjLAsa8efNQ79u3r9OoQkLbtm2ddvPNN2OfofXRtEyePBl12n/ZokULp1G1jvbt22/+wAoh9MSc9iXNnDnTaffee2/i98qtFFFQUIBroxtDewBDYx48eLDTaO2HqtSEyF1z2WabbRK/trB+ChvLsmXLnHbaaac57Zhjjsk0liQsXrwY9YMOOshptWrVctq4ceOcFtormrsvsKCgAPdTbwztZaWKRGZmN9xwg9No/Z4qeND5Y8Z7p2N7dWnM5GcwM/vpp5+cdt999znt/vvvd1rovLj00ks3+XexYsWwAs/G0PUXWqOmc5wqwVBVndatW2OfvXr12uTfBQUF0fs1Heett94a29L3+MgjjziNxkzrnWab7l0vXrx4oT6bvEyW9IHNuETQwoULnbZ06VKnFfVSaqjcDpXzog3QVHZoS/Hzzz87bcmSJZvVZ1EffzqmRbmZPx9QWTY6d0MbzYsKuomY8bVGf/CEJgEiX+cFhU2Y8Zjphk8TQ1ET+ux0/FesWOE0+mz0x5ZZuu8kX9B5S+X/Vq5cia/fEvYXKmVI9/A0310IPYYVQgghImiyFEIIISKkfgz72WefOa1hw4bYltalWrZs6bTrrrvOac8++yz22b17d6fF9sfQYwPKczTjrE9aH6H1v2nTpmGfDRo0KHR8SXn99ddRHzhwoNM++uijRH0+/fTTqDdp0mSTfxcvXjy6NkV5n6FjMn78eKd98sknhfa/gcsuuwz1Cy+88L//XaxYMdtpp50S9ZfLrFmzUP/222+ddv755zuNHg19+OGH2Gf9+vX/+99J1oWJRx99NHFbOu70SJPamZkdeuihm/y7WLFi0RzTp556ymlJvsMN0Drm22+/7bTq1atjn1n2wtK6Gb2nmdlFF13ktLPPPttpdK0NGDAA+8xd2kqSh5xmD+3JJ5/sNDp+11xzjdNC682551GSPaR0nL/44gtse/zxxzutc+fOTiO/Ruh+v/Exix1j/bIUQgghImiyFEIIISJoshRCCCEiaLIUQgghIqQ2+JB5IRS2S2aeXOOIGRuBQhvDsyzW06bt0D7LUaNGOY32MZYvX95pVLA5K2QmadeuHbbt0aOH0xo3buy0sWPHOo0W+s3Mvvrqq03+ncRgQEaPkBmANmPTXqgbb7zRabfeeiv2uXGgRNKAavpuQ8WfadN2zZo1nVa3bl2nHXjggdjn7bff/t//TnJuz5gxw2m5G9g3cMsttyQaGxWPDgUdNGvWbJN/JznO9erVcxqFk5glH/OJJ57otNDxy3LPoPvctddei21HjhzpNCpuTgWXQxvwczfzZw3sDxmI9tlnH6eRgYYMj02bNsU+c+eBJGMmMw99t2abmuE20KFDB6d16dLFaTVq1MA+Nw63j41XvyyFEEKICJoshRBCiAiaLIUQQogImiyFEEKICJoshRBCiAip3bAU3UYuLzOznj17Oi0UZZRLyBGVhUqVKjmNSmyZmV1yySVOI0dn5cqVnUYlkbJCcX+h5Hxy3lGEILlh99prL+xz1113jQ3RQVGIFHVmZvb+++87beedd3YaxQr2798f+9zY2ZYUihB85513sC1VYHjvvfecRg7bUHWDtCXnhg0blrjtLrvs4jRyP9N3dNJJJ2GfZcuWTfz+G6A4zCeeeALb0rVGjuNXX33VaZ06dUo9thAU0/jpp59i2zfffNNpZ511ltMoRnHQoEHYZ5YKPHRvpbg6M3YYk9uXohCHDx+OfcbiMAmqTEX3ETO+riiCkHYSPPzww9hnLKpxY/TLUgghhIigyVIIIYSIoMlSCCGEiKDJUgghhIiQ2uBTokQJpx1wwAHYNrSInwvVBPzPf/6TbmCFULp0aaeFTCLt27dP1GeotmS+IOMHHXuzTWPeNrB27VqnUb265557DvvMEq9FxzQUAUhGMTLokMHg8MMPTz22EGQwmD17NrYlIxVRp04dp/373/9ON7AAu+++e+K2IZNOLmRMo5jBrOTWZjQza926Nba98sornbZw4UKnnXDCCU6bNGkS9tmoUaPICD0VK1Z02sEHH4xt58yZ4zSK7RsyZIjT2rRpk3psIX755ZfEbem8p+983LhxTstaJ5ag+FO6n5kZ1nolc+mee+7ptBYtWmQY3abol6UQQggRQZOlEEIIEUGTpRBCCBFBk6UQQggRoeCvUCxMCkKpHr1793YapbRQWsYdd9yBfZLxJYsZJWR+mDBhgtPI9PPoo4867ffff089jjQsWLAA9ZUrVzrt4osvdhqlFoUSRJKQe+pQ+sq8efPwtZQmtGTJEqeRmSdkSsoCGR0+/PBDbFuuXDmnkemHDGtpknfSsnTpUtSpZmTbtm2d9thjjzmNahsmJfe8oGQZSkMyM2vevHmi9yAT1bnnnottQ3ph0G0xlMK01VbeJ0nGmDFjxjiNroN88uOPP6JOdTTpPCLD1ZNPPrn5A8sAHX+qu9qqVSunkQkrLfplKYQQQkTQZCmEEEJE0GQphBBCRNBkKYQQQkRIneBDhEojUfmiZs2aOY1MFiFjyD777JNqbCGotIuZ2W677ea0evXqOY1SLN544w3ss2nTpk6jBfYY1apVQ50Wr+n4kSnpjz/+wD632Wab6HhyjVWnnXaaa0PpLWZ8THr16uW0iy66KDqODeSmPhUrFv9bsEKFCk7r2LEjtk2awkNl3kJkGXMuVIorzTjIzLNmzRpsm6UMExnQQokqVJKNkqu+/PJLp1HqTlbINEhGnhDPPPOM02rUqOG03377DV9PnzmLkTFUao++E7pfU1JSCDLgFC9evNDXUMJXqGwd9TV58mSnUVJZyJwVG9/G6JelEEIIEUGTpRBCCBFBk6UQQggRQZOlEEIIEUGTpRBCCBEhL25YiogzMzvllFOcRo7M+vXrOy3koswXFD1lZnbNNdc47aOPPnLa1Vdf7TRyYZllc74SoWTCBx980GnkgsunW5CgGqQhdydFoFGtRnIQhpxt+XCWmoUdiuPHj3dau3btnFapUqXE75XF4ZgLOUPNzD799FOnDR48OFGfWVyvG8j9TFTv9uabb8bXUlTg6tWrnUZu2mOOOSbpEKNQdGWoniydj++++67TRo4c6bRtt902w+gYumeGrgE671asWOG0Ll26OC10H0rjLN0AjS9Uy5jakuufzt3QfCI3rBBCCJFHNFkKIYQQETRZCiGEEBHysmYZSragdBRKhqEEkiQJMptDaP2B1voooYhSJtIkfOQTOn6hdbd/CqVLl3YaHfss6yCbS2gdkdKdypcvX9TDiRI67yjxaYcddijq4SSiTJkyqNMxpjShUDLNP4XKlSs7bbvtttsCI2HoHKfvJOu6/+aMIw10PtP9MB/egLzUsxRCCCH+J6PHsEIIIUQETZZCCCFEhNSLbOvXr3ca7T8z4woCtH/pyiuvdFrLli3TDi0I7bH57LPPsG3//v2dNmjQIKftt99+Tgs90c7yvJz6Ch3nCy+8MFGfzz//vNMaNGiQbmApCVVioeO8ePFip40YMcJp7du3xz5zj3OS9U5aDwvt1/v888+dRnuEaQ/gySefjH3uvPPOsSFGoWvSjI8n7Zt7/PHHnUZ7Xs3S7aUtbHy0d9mM9znPnj3babQ/kdqZ5We9yiw8Zrp/NWrUyGlDhgxJ/F50zGKeCLpn/PTTT9i2d+/eTvvwww+d9sgjjzjt0EMPLXQcRcWoUaOcdv311zuN5p1WrVpt9vvnxZFCZVbMzBYtWuQ0Mp6sXbs2H8NIBU3aZnyDCbX9u6HN2WZmCxcuTPT6UDmuoiT03X733XeJtNBnzhd0g6Hz1oyPM5Vqo/JHoY3WRQndcL/99lunFXUACBEyoNGxp+O+JcwyofsAjblq1apFPZxEhM47KotIx/mfZBT85ZdfnEZjLqr5RI9hhRBCiAipf1k+8MADTrvhhhuw7dChQ51G0Xjdu3d32s8//5x2aEEobu7FF1/EtvRYjrax0C+SfD3uMeMIs9CjvObNmzutVKlSTqPixS+88AL2SZFtsc9Hf3mHIgBvv/12p82aNctpVHy2Zs2a2Cc9Go9B32Oo/06dOjlt4sSJTqPHWR9//DH22aZNm03+neUcCj2eowLntA0qTTxfksewucd02LBh7jV9+/ZN/J60DeOkk05yWj6vP4qwe+yxx7AtLQvQL0t6clKlShXsM8uWDYp+mz59Oralosm0DaN169ZOy+cGCvqFGzo36JHwxRdf7LRbbrnFaYcddhj2SddDCP2yFEIIISJoshRCCCEiaLIUQgghImiyFEIIISKkNvjQguxLL72EbcnCS8aOAQMGOC2fexYJMmaYsXFg7733TjSOUJ3FLPmmtJjdpEkTbPvUU08lek/a/0d198x4r2Hs2FPeLu1DNOPtFTNnznRa7dq1nUbbNcyymSIo43fcuHHYlvbmvvzyy04jo1NozGnPZ9rmEbLKP/fcc07r2LGj02gbBhn5zNhwlWswyv1Macw8xEEHHeS0tm3bOi20hY2+4xh0n6PcWjOzXr16Oe3+++93GtVZDN3nspzLM2bMcFqo1vCBBx6YaCx0HEL7erNkY7/11ltOmzt3LralGqi0tYzGl8bIE0K/LIUQQogImiyFEEKICJoshRBCiAiaLIUQQogImiyFEEKICKntS2eeeabTqDK1GTvnpk2b5rTrrrvOaaHQb3Jc5hNyTVFcHpHF9RqCnH2hIGd6X4quori8SZMmYZ9du3aNDdFBTs2QQ3j06NFOe/PNN51GFV9CEWFZnNIUq0gV4804to3ixO666y6nNW7cOPXYCDoXKVbSzOy9995zGrmsjzjiCKeRs9LM7NRTT40N0dGtWzenharRUJUMcmyPHDnSaVlcryFWrFjhtFq1amFbqgZE3xOda+XKlcswOubggw92Gh0nM7MpU6Yk6pPuGaHiBnTPiUFRiz179sS2VASAKimRa5liTM3YoRxCvyyFEEKICJoshRBCiAiaLIUQQogImiyFEEKICKkNPmTmCZk4qP7b7NmznbbXXns5bc6cOdjnHnvsERtiIkJxUjvvvLPTFi9e7DQyGoXinkKGkcKgGpo0DjOuZk6L7WRQCEVL5QsySphxXBl9jtdee81pnTt3xj4rVKiQcnR8nELxcQcccIDTKFLulVdecVpozGlqSZpxrb5rrrkG21JMY58+fZxGkWNDhgxJNa7CIDNXKOatR48eThszZozTfvzxR6eFIgWzGO/ILETvaWa2dOlSp1E9WooQJBOWGUcQxqhYsaLTqP5oiDp16jitVatWTktjiolRr149p1GtzdD7kumRaonmY8z6ZSmEEEJE0GQphBBCRNBkKYQQQkTQZCmEEEJESG3woQXVNKk6e+65p9MeffRRp1FaipnZHXfc4bRYcgsZNkKL/oMHD3baBRdc4DQy7YSSZV5//fXo++caHqivkMHgl19+QT2XJ554wmkhowXpseNMqSVkmDLj2px0bhx99NFOC9Xg/Ne//lXo+Aj6nCFzBdUtXLJkidOuuuoqp5133nnYZ8zgk1ubb+zYsa5NyKz2xRdfOG3q1KlOI2Na69atCx1XGpImYJmZtWnTxmmU9vP11187rUGDBqnGVRh0fc+fPx/b7rfffk6jurgjRoxwGiVUmXGqWYzvv//eafR9m7FxjgyEd999t9OaNm2KfVJyTuyeQbUnFy1ahG2p7jGlT51yyilOe/rpp7HPNPcM/bIUQgghImiyFEIIISJoshRCCCEiaLIUQgghIqQ2+JCZZ9myZdh25syZTiPjyieffOK0efPmYZ+0IBwzEJBhI1ROZtasWU6jNI4JEyY4LbRYnJvwUbx48WBZsw106NDBaeeeey62peSNbbfdttD+N0DpKmbZyl1RGZxx48ZhW0rDoYV9SnKqVq1a6rGFoLJJH3zwAbYlAwUlUhFkfjDzBqPc457778svv9z1QZ/BzKx06dJOIwMbHc+6detin5QIEzIYFUYojYqMJ2QGo/GlSauJjZlSySjpyIyTg+rXr+80Mujls0QXXbNUtsvM7KOPPnJa+/btnfbOO+84je7XZv44FBQUWKlSpbBtYXz33XeoN2zY0GlkkKLvNsv9zPW72T0IIYQQ/8PRZCmEEEJE0GQphBBCRNBkKYQQQkTQZCmEEEJESO2GJV599VXU77zzTqf99NNPTlu5cqXTHn74YewzTXTWBtatW+e0oUOHYtszzjjDaSHnbC7XX3896uXLl4++NtetVaNGDdfm3nvvxdeSS7ZZs2ZOo8/WqVOn6NiSQjXjVq1ahW2T1iU95JBDnEbHxsy7IZO4NCnqLRRNR/FxBH1PVEvUbNPjU1BQ4Ooo5sYihupiElRn8YcffnAaRUiGarP+8ccfTqPaqxtDLtWQo5LuJXQfIXdx6PtO45LdALnVqZaomdmll17qtGuvvdZp1atXdxpFYWaFohOHDx+ObSkS7oorrnAa7V4IHc/c+3jx4sWjbliqQUs1Ys04eu+ee+5xGu2YIPd9WvTLUgghhIigyVIIIYSIoMlSCCGEiJCXNcvQc2l6Hk3rG7nrNGbJE2iyElqToTEnTYxJuraZFTpOZrx+Q+uktKZY1FCKjFnyY0rfR5bEmBCU7FG5cmVsS+XpiND3FHv/fKSMbAwdJ1qDiq05FgWhMmhVq1Z12pY4b4nQPalixYpOo1QlOq9CpQLzRcjjQWOma5Lahb6P3M+S789G1xWNj9Ys8zGWgr9CBQ2FEEIIYWZ6DCuEEEJE0WQphBBCRMjLmmWo6kHv3r2dRin2p59+utOuvPJK7DNL1QN6hr1kyRJs279/f6e9+eabTttrr72c9thjj2GftG4Xe4ZO++FOPvlkbEt9XXLJJU6jCgRURcYs23GmfX0XX3wxtv3000+d9sADDzht7733TjyOWAWPJK8xC++zfP755502ZcoUp9E6K1WcMPNVJ2L7iGm8a9euxbZ0DtCxGzZsmNPomjHLtr5J59Lq1auxLe1lpCowN910k9PKlCmDfdL+wyzr3gsWLED9hBNOcBp95okTJzottA5Kr8+y7haqoEPVay644AKnpdmHTedmluP87LPPon7++ec7jdYxu3Xr5rQzzzwT+8ytlFLYePMyWYY2qdINYuHChU5bsWJFPoaRCirBY8aTKI25bNmyTsuy+TkEjY9KWJnxRRS6gRYlNObQJPHtt986LamBpqih4AwzPg9C51HWdlkI2Q7oj5eiNpQkJTTm5cuXO43KeVE4QmiCzxeh/qmkFN0LtoQ9JHRN0b0k9AfM301oHHT90Q8Rmk/ycW/WY1ghhBAigiZLIYQQIkLqx7Dvv/++044++mhsS/mk9Cjirrvuctq0adOwz9y1woKCguieTMoa7NWrF7Y97LDDnDZ//nyn0ZoJPVo0C6+lFMZLL73ktGXLlmFbyj2kY0p72Bo0aIB9Zllr6NOnj9OmT5+ObWk9+6yzznLa008/7bSaNWumHlsIWtekc9yMx0znC61jzpgxA/ts0aJFbIibQON94403sO24ceOcRvmalNO6zz77pBpXYdC5FLomXnnlFadRTiutr11zzTXYJ2Wyxpg3b57TQrm8tHRDj93JDxHKm83yuJweE9PapJnZnDlznHbqqac6jfZUHnHEEdhnvvYJd+/eHfV+/fo5jfauki8mtAyS5j6nX5ZCCCFEBE2WQgghRARNlkIIIUQETZZCCCFEhNQGn9GjRzstZAYYM2ZMoj6/+eYbp4U2AOcu4idZVKYx08ZVM7Pbb7892p8Zm2pC+/OymGUolD20sbZv375O69Chg9PyHdSdCxkxKAjBjM0YY8eOdRqZZUKGjSzHmUwRoZD3unXrOu2zzz5zWo8ePZx20UUXYZ9pi5nTvtXQOXvSSSc5rVWrVk4jM0s+zxUq7k4GNjOznj17Oo0MG7RxPZ/GLzIYUlCIGZuSKAxgwIABTiPTj5kPq0jCxx9/7LSQUfLmm292GoVukEGoUaNG2CcVdIhB53OoyMWRRx7pNCoW/swzzziNrkkzDqwIoV+WQgghRARNlkIIIUQETZZCCCFEBE2WQgghRARNlkIIIUSE1G7YGjVqOO3OO+/EtuQerF27ttPIERiKVIpF2xH16tVz2uDBg7EtOTLr16/vNHJ+nXbaadhnFpdm8+bNndakSRNsSxGCX3/9tdPIrRqqShAq3VUYV1xxhdN23XXXxK+nSi4UIRiqIJDlOK9bt85p5KYzM9tjjz2cRpU9qLxcy5YtU4+NePLJJ51GcXVmZo8//rjTnnjiCad99dVXTjv88MOxzyzHmOLgpk6dim3JJX3dddc5jRzuVapUST22EKtWrXJayCFMkZEUYzh8+HCnhdyqrVu3jg3RMWvWLKdRuTgzvr9S3B2VIpw5cyb2mcUNS2700PVNbuRffvnFabllt8z4+0yLflkKIYQQETRZCiGEEBE0WQohhBARNFkKIYQQEVIbfM455xyn1apVC9uOGDHCaRRVRgaVpk2bph1aEKqDRrFfZmYTJkxw2o477ug0MnZUrFgx/eACkBknBJk2yIxCfWYxbISghfUQZCz69ddfnUYGg1AcVha22247p61duxbb/vbbb04jIxbVWsyXkWrkyJFOa9++PbadPHmy04YNG+Y0ikakCDwzszp16kRG6CHDVKifL7/80mkrVqxwGkWzhb43itCLQfU26VwxY5MKceyxxzpt7ty52DaLwYdqNm6zzTbYluI0yWB3zDHHOI0MW1mhY0p1kM3Mzj77bKfR/YEMdl27dk0/uBz0y1IIIYSIoMlSCCGEiKDJUgghhIigyVIIIYSIkNopQQuyRx99NLYtX7680yZNmuQ0WnxdvXp12qEFKV26tNNCi8hkJqDFcKqd9/7772OfZICK1QukxIlly5Zh24EDBzrtoIMOchqZeUJ1Q7PUBkxjvKFjReOj1I7Zs2djn3vuuWfi9y+Mo446CnVKtZk/f77TKHWoYcOGmcaSax5ZuHBhojGYmT399NNO++OPP5xGpqHQNZ3E4JNrNLnvvvtcG6pxaWa2/fbbR/s34yQjMltl5dBDD03clmpXdu7c2WlUozJ0/WWB6kxSwo2Z2fTp051G1zzdp0LXXxbo3hwyw9G94OSTT3Zau3btnBaaT0qVKhUb4n/RL0shhBAigiZLIYQQIoImSyGEECKCJkshhBAiQv6iUIBRo0Y5jRKAli9f7rRQSgSVw8kCpbGYcekf0p599lmn/fTTT9hnzMxj5lOMFi9e7NpQMoyZ2Zw5c5xGJbqoZBOlXZiZXXbZZainhRKRzDihhI7T5Zdf7rRQ2a+N36t48eKJUpBo4T+UqnL33Xc7jcwrn332mdOyGnxyTU9UQi5klnnooYecNnHiRKf9+OOPTstSCm8DuecylW6ja8qMz5err77aaVdddVX0fTeHSpUqOa1q1arYlsr9kcmLkrYuvPDCDKNjdt99d6eF7nN9+vRxGpld6Po499xzsU9KMoqZ/sjMQ2UczTh17d5773UaJbalMfKE0C9LIYQQIoImSyGEECKCJkshhBAigiZLIYQQIoImSyGEECJCXtywoRg2qk1HLk+qQ0d11PIJxYaZmX333XdOGzp0qNNozOT6S0quE5TciLNmzcLXdurUyWkU1zVz5kynnX/++UmHGIVczYMGDcK2VC+QnK+NGzd2Gn0Os02jCrfeeutEbliq99exY0ds261bt0Tjq1KlitP+85//YJ/FixcvdHy5btg2bdq4NiHH4/Dhw51GNWbJKRiqg5iEXAfkcccd59rsvffe+FqKiQu5UP9u7rnnHtTPO+88p5Fbt23btk7LZ0QfxXI+9dRT2Pb00093WoUKFZxGrvhQ/dQsdWYp3pCOkxnfh6ntO++84zQ6r8yS7VTYgH5ZCiGEEBE0WQohhBARNFkKIYQQEfKyZkmllczMKlas6LSSJUsmfn1REnq+TmPecccdnUZrivn8HLSWRWthZlwKjdYEd955Z6eleWYfgz4/rYOYme22225OozHTcaayPmb/d51yA1nWTzaw0047oV6tWjWn0efbnPSbLIS+QzqXk5bAKmo2/q42hs7xf/qY6RygUn+0hr4552kSQuciHWdKxqL7dT7vGUQobYfOZ7pWqYxkPij4K58ZUUIIIcT/QPQYVgghhIigyVIIIYSIUKQPzDt06OC0gw46yGmUvB96bp2vZPtQZYkzzjjDafSsnFL7mzZtWug4NpdQdQnak0r75B544AGnhSp40NP52FoF7fcL7U17+eWXnUb7NGmP3R133IF9JtlXmQtVVaDv1sxs9uzZTqO1qa5duzrt1FNPxT7T7iFct26d0y666CJsu3TpUqfRPmLaj7nPPvukGldh/PHHH06jPbVmZm+99ZbTaB833Ud69OiBfbZo0cJpofXHwgitWNHno72lTZo0cdqll16aehwh/vzzT6e98MIL2PbWW291Gh3TvfbaK1E7M/YhxPbrrlmzxmmPPvootiWdqlDRPtBmzZphn7QmG6JIJ8tFixY5jW4uW2LZlE5wM76Z0CQR2ghelIQ2ttNxLlGihNPoYson9D3+/PPP2JbCKejmTje10HHIAo05VB7u+++/dxqVZaNJn/7Iyxeh0nBUeos+Q+haKEpCQSZU2orOi5o1azqNbrx/B3QO/fDDD06je19RQ38MmvF5QN/JqlWrnEZ/sGWFjt0vv/yCbWnM9EOGzoN8zDF6DCuEEEJE0GQphBBCRMjLY1h6DGhm9tVXXzmNnpUPGDDAaUX9aJYyPc34pz5p999/v9NCz8Wz5GzSo8Zy5cphW1qTpfW1J5980mlnnnkm9kmPcWPQ9/34449jW1pnpf10tKZA+0Wz8u677zrt2Wefxbbjxo1z2v777+802m9atmzZDKPzUKbxmDFjsO28efOc9sYbbzgtdC3kCzr/Q8eYjtPdd9/ttEmTJjmN9kObZdv/TNdfqB+6P3z99ddOo8fz/fr1wz5D13ph0LlMHgwzvr6feOIJp9E1GcpOzrIOTI+m58+fn/j1vXr1chp9d59//jm+PvfcL8yXoV+WQgghRARNlkIIIUQETZZCCCFEBE2WQgghRITUBh/aYxMysNCCO+3boaKlIbIs1tNi9scff5y6n42hDfCbUzA3lzSfM2nQNJll8hn6TYvj33zzDbZt166d02gvIoWr//rrr9hnbtskgc+0t6xy5crYtlatWk4jI0ft2rWdlq9wZzKTkMnIjDeJk6GCggAOPPBA7DNfoeahPYdUyHzYsGFOO/roo51GBc/Nst0z6DWhPYu08Z/2WVLQQxYjT4ixY8c6LTRmCt6YMGGC0+h+H7qusgSsL1iwwGnPP/88tu3du7fT3n//facNHjzYaXRszPze88ICbvTLUgghhIigyVIIIYSIoMlSCCGEiKDJUgghhIigyVIIIYSIkNoNS5FGpUuXxrZUZqtChQpOo7i2UNxaFmcb9U+uwhDkKjzppJOcFqrqUbx48cTvtYE0pcioAsOMGTOcRgn9+RwzVbkIfY9nnXWW08hBSNqsWbOwzzSu6g1QxY3QuXH22WcnakvfE8XMmfG5VRjkvg2dF3RdUnmle++912lUzs0s7DgtjHfeeSdx29GjRzuN3MWPPPKI07p164Z9hsrQFQZVvnj44YexLUVfJiVUvSiLS50+Z6g0XP369Z127bXXOo0+W9pztjAaNmzoNDoHzMyOOOIIp9HuimeeecZpVLYrLfplKYQQQkTQZCmEEEJE0GQphBBCRNBkKYQQQkRIbfChBekvvvgC2y5evNhpVIuQFmlDtdGyGHzIePL6668nfj2Njxams5hiQpDxZPr06dh27ty5TqN4tX333ddpWY5niJ9//tlpZD4yY7MMGTT23HNPp4VMSVmoV6+e0yhKzczsvPPOS/T6qlWrOi1kcjnhhBNiQ9yEww8/3GkhY0tSk0jfvn2dFoqjy8LKlSudFjrvBg4c6LQ2bdo4jeL4yAxmls3gQ58/FMNGMZIE3fvoOjfLZvCh2pWhe1KrVq2cRiYYMlflEzLlUfyiGd+HiSOPPHKzxhRCvyyFEEKICJoshRBCiAiaLIUQQogImiyFEEKICHlJ8CGzixkv7JO2dOlSp9FieFaor5BZhqD6ibQA/5///Adfn8VEQ7UxQ8eEjA1US5QW+7PUoAtB5wHVzTMzO+6445xGJhhKrCFTTVaoFmQokYXMCJ999pnT6JiWLVs2w+g8VGszZIYj5s+f7zQyTNF1mhUy40yZMgXb7rfffk4bMWJEovcJpUXliwMOOAD1PfbYw2kffPCB0yi9jFLOslK+fPnEbT/55BOnkXmssPqO+WDq1KlOu+aaa7DtnDlznNa4cWOn3XbbbU47//zzM4xuU/TLUgghhIigyVIIIYSIoMlSCCGEiKDJUgghhIiQevU2TUoNpbcsWLDAaYMGDXIalQ0y4wVnMsNsDCVstGzZEtuSyYSSb4h8puHQ56RUHjM2CZBBY+LEiU476qijsM+//vprk38XFBREDRRVqlRxGqX6mJm9/PLLTuvXr5/THn30Uafl8ziTuSVkPlm0aJHTyDhA50uLFi0yjM5DKSbDhg3DtpR8k9R0R0airJDx7cknn8S2gwcPdtqzzz7rNEodqlu3LvZJ33HsPkZlqOg+Zcbl8MgASEln+Uz9InKv4w1QytTy5cud1qhRI6eFjkO7du2clsZ8toFq1aqhvm7dOqf17NnTaXS+yOAjhBBC/A1oshRCCCEiaLIUQgghImiyFEIIISJoshRCCCEiFGmW0dq1a51GteXq16/vtFCNuN9//z31OMhF1axZM2x73333OY2iqyiS6cILL8Q+t99++8gIkxGK06MYvPXr1zuNHMAhh+uaNWs2+XeSWLw0rseRI0c67eqrr3Ya1Xukz2aWLZqL6rPefPPN2JZiBa+44gqnkVMz5OAl13FhlC5d2mmzZ8/GtuRarFGjhtPOOeccp1GEmxm7K2NjLlOmjNNmzZqFbb/88kunkZPxhhtuKPQ9N4bO5dg1mSYGklzgFI1Hx4Fq/pqZ7bLLLk6Lnd90XYTq9n777bdOGz16tNMaNGjgtFB0Y+79vqCgIOqGrVOnjtNOPfVUbEtjITp27Oi0UC1Mup5C6JelEEIIEUGTpRBCCBFBk6UQQggRoUjXLOlZPq15UOmjooYSNsx4zJSyQWPOZ7krIpT2UbFiRafR+kaa5Jvcz5L1s1GpMDNOSKE1naKGPhetq5vx8dsSY86F1rfMOAmFknnoM+QzWYaOcaicVO76oplZuXLl8vr++b5O6bygclzkLSjqBJ9Q6lcoJSeXSpUqOS3kc8hynKlNaD5IOmY6t/LxnRf8FcpDEkIIIYSZ6TGsEEIIEUWTpRBCCBFBk6UQQggRQZOlEEIIEUGTpRBCCBFBk6UQQggR4f8AWuw4Y5kgNF0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digits_new = pca.inverse_transform(data_new)\n",
    "plot_digits(digits_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results for the most part look like plausible digits from the dataset!\n",
    "\n",
    "Consider what we've done here: given a sampling of handwritten digits, we have modeled the distribution of that data in such a way that we can generate brand new samples of digits from the data: these are \"handwritten digits\" which do not individually appear in the original dataset, but rather capture the general features of the input data as modeled by the mixture model.\n",
    "Such a generative model of digits can prove very useful as a component of a Bayesian generative classifier, as we shall see in the next section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.12-Gaussian-Mixtures.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "encoding": "# -*- coding: utf-8 -*-",
   "formats": "ipynb,py:light"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
